%!PS-Adobe-2.0 %%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software %%Title: positivefin.dvi %%Pages: 21 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips positivefin.dvi %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2002.01.09:1936 %%BeginProcSet: texc.pro %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3 1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{ rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B /chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{ /cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{ A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse} ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17 {2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{ 1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop} forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet TeXDict begin 39158280 55380996 1000 600 600 (positivefin.dvi) @start %DVIPSBitmapFont: Fa eufm10 10 1 /Fa 1 104 df<02101310027C1370903901FF80E04913F3010F13FF133F5BD801FC14C0 3803F80FEC003F150F5B1207A2151FAF6D133F6DEBFFE06D5A9038FF079FEC8F0F6C13FC 6C01F813F014F06C13E0EB7F8090383F0007131E4914E0017014C0485A486C1480486C14 00486C130648B45B007FEBC01800E7EBF0300003EBFFE0C6FC6D5B011F5BD903FEC7FCEB 003824387FA62A>103 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fb cmbx10 10 9 /Fb 9 58 df<49B4FC010F13E0017F13FC9038FF83FE4848C67E4848EB7F804848EB3FC0 4848EB1FE0A2001F15F0A24848EB0FF8A3007F15FCA500FF15FEB3007F15FCA4003F15F8 A26D131F001F15F0A2000F15E06D133F000715C06C6CEB7F806C6CEBFF003900FF83FE6D B45A011F13F0010190C7FC27387CB630>48 D<141E143E14FE1307133FB5FCA313CFEA00 0FB3B3A6007FB61280A4213779B630>IIII<001C15C0D81F80130701F8137F90B61280A216005D5D15F05D1580 4AC7FC14F090C9FCA8EB07FE90383FFFE090B512F89038FC07FC9038E003FFD980011380 90C713C0120EC813E0157F16F0A216F8A21206EA3F80EA7FE012FF7FA44914F0A26C4813 FF90C713E0007C15C06C5B6C491380D9C0071300390FF01FFE6CB512F8000114E06C6C13 80D90FF8C7FC25387BB630>II<123C 123EEA3FE090B71280A41700485D5E5E5EA25E007CC7EA0FC000784A5A4BC7FC00F8147E 48147C15FC4A5A4A5AC7485A5D140F4A5A143F92C8FC5C147E14FE1301A2495AA31307A2 130F5CA2131FA5133FA96D5A6D5A6D5A293A7BB830>I57 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fc cmr7 7 3 /Fc 3 53 df<13FF000313E0380E03F0381800F848137C48137E00787F12FC6CEB1F80A4 127CC7FC15005C143E147E147C5C495A495A5C495A010EC7FC5B5B903870018013E0EA01 80390300030012065A001FB5FC5A485BB5FCA219267DA521>50 D<13FF000313E0380F01 F8381C007C0030137E003C133E007E133FA4123CC7123E147E147C5C495AEB07E03801FF 8091C7FC380001E06D7E147C80143F801580A21238127C12FEA21500485B0078133E0070 5B6C5B381F01F03807FFC0C690C7FC19277DA521>I<1438A2147814F81301A213031307 1306130C131C131813301370136013C012011380EA03005A120E120C121C5A12305A12E0 B612E0A2C7EAF800A7497E90383FFFE0A21B277EA621>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fd cmmi10 10 5 /Fd 5 114 df<1760177017F01601A21603A21607160FA24C7EA216331673166316C3A2 ED0183A2ED0303150683150C160115181530A21560A215C014011580DA03007FA2020613 00140E140C5C021FB5FC5CA20260C7FC5C83495A8349C8FC1306A25BA25B13385B01F016 80487E000716FFB56C013F13FF5EA2383C7DBB3E>65 D<902603FFF891381FFFF8496D5C A2D90007030113006FEC007C02061678DA0EFF157081020C6D1460A2DA1C3F15E0705CEC 181F82023815016F6C5C1430150702706D1303030392C7FC02607FA2DAE0015C701306EC C0008201016E130EEF800C5C163F0103EDC01C041F131891C713E0160F49EDF038183001 06140717F8010E02031370EFFC60130CEE01FE011C16E004005B011815FF177F13386001 30153FA20170151F95C8FC01F081EA07FCB512E01706A245397DB843>78 D<003FB56C48B51280485DA226007F80C7381FF00091C8EA07C0604993C7FCA2491506A2 0001160E170C5BA20003161C17185BA20007163817305BA2000F167017605BA2001F16E0 5F5BA2003F15015F5BA2007F150394C8FC90C8FCA25E4815065A160E160C161C16181638 5E127E5E4B5A6C4A5A4BC9FC6C6C131E6C6C5B6C6C13F83903F807E06CB55A6C6C48CAFC EB0FF0393B7BB839>85 D<90390F8003F090391FE00FFC903939F03C1F903A70F8700F80 903AE0FDE007C09038C0FF80030013E00001491303018015F05CEA038113015CA2D80003 1407A25CA20107140FA24A14E0A2010F141F17C05CEE3F80131FEE7F004A137E16FE013F 5C6E485A4B5A6E485A90397F700F80DA383FC7FC90387E1FFCEC07E001FEC9FCA25BA212 01A25BA21203A25B1207B512C0A32C3583A42A>112 D<02FC13C0903803FF0190380F83 8390383F01C790397E00EF8049137F485A4848133F000715005B485A001F5C157E485AA2 007F14FE90C75AA3481301485CA31403485CA314075D140F127C141F007E495A003E137F 381F01EF380F839F3903FF1F80EA00FC1300143F92C7FCA35C147EA314FE5C130190387F FFF0A322357DA425>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fe cmti10 10 53 /Fe 53 123 df<04FFEB03F003039038E00FFC923A0FC0F01F1E923A3F00783E0F923A7E 01F87C3FDB7C03EBFC7F03FC14F8DA01F813F905F1137EDC01E1133C913B03F00003F000 A314074B130760A3140F4B130F60A3010FB812C0A3903C001F80001F8000A3023F143F92 C790C7FCA44A5C027E147EA402FE14FE4A5CA413014A13015FA313034A13035FA313074A 495AA44948495AA44948495AA3001CD9038090C8FC007E90380FC03F013E143E00FE011F 5B133C017C5C3AF8780F01E0D878F0EB07C0273FE003FFC9FC390F8000FC404C82BA33> 11 DI< 04FFEC3FF00303903AE001FFFE3F923B0FC0F007E01F923C3F00780F8007BF923C7E01F8 1F001FFFDB7C03013E5B03FC027E14FEDA01F85C17F0DC01E0141E912803F00001F8EB00 FCA21A01170302074B14F85D1A03A2050715F0020F5D4B1607A21BE0010FBAFCA3903E00 1F80000FC0000FC0A21A1F023F141F92C7491480A21A3FA24A023F1500027E92C7FC62A2 1A7E02FE5C057E14FE5C62A205FE130101015D4AEFF838A219030103020116784DECF070 5CA21BE0010714034D14E14A933801F1C0F100F3F27F80010F4A48EC1E004A94C7FCA34A 495A131F5F001C903803801F007ED90FC090CAFC133F26FE3E1F133E013C5C017C5C3AF8 780F01F0D878F0EB83E03A3FE003FF80270F8000FECBFC504C82BA4A>15 D<13F0EA03FCEA071EEA0E1F121CA212385B1270A25BEAF07E12E013FEC65AA212015B12 03A25B12075BA2000F13E013C013C1001F13C01381A2EB83801303EB0700A2130E6C5AEA 07F8EA01E0132679A419>I<00C01306A3140E140C141C14386C13706C13F0387001E038 3C0F80383FFF00EA0FFCEA03F0170E69B92A>21 D 44 D<387FFFF8A2B5FCA214F0150579941E>I<120EEA3F80127F12FFA31300127E123C09 09778819>I<15181538157815F0140114031407EC0FE0141F147FEB03FF90383FEFC014 8FEB1C1F13001580A2143FA21500A25CA2147EA214FEA25CA21301A25CA21303A25CA213 07A25CA2130FA25CA2131FA25CA2133FA291C7FC497EB61280A31D3877B72A>49 D65 D<0107B612FCEFFF8018C0903B000F F0001FF04BEB07F81703021F15FC17014B14FEA2023F1400A24B1301A2147F18FC92C712 0318F84A140718F04AEC0FE0EF1FC00101ED3F80EF7F004AEB01FEEE07F849B612E05F91 39F80007F0EE01FC01076E7E177F4AEC3F80A2010F16C0171F5CA2131F173F5CA2133FEF 7F805C1800017F5D4C5A91C7485A5F49140FEE1FE0494A5A00014AB45AB748C7FC16F816 C037397BB83A>II<0103B612FEEFFFC018F0903B0007F8000FF84BEB03FCEF00FE020F157FF0 3F804B141F19C0021F150F19E05D1807143F19F05DA2147FA292C8FCA25C180F5CA21301 19E04A151FA2130319C04A153FA201071780187F4A1600A2010F16FEA24A4A5A60011F15 034D5A4A5D4D5A013F4B5A173F4A4AC7FC17FC017FEC03F84C5A91C7EA1FC04949B45A00 7F90B548C8FCB712F016803C397CB83F>I<0107B8FCA3903A000FF000034BEB007F183E 141F181E5DA2143FA25D181C147FA29238000380A24A130718004A91C7FC5E13015E4A13 3E167E49B512FEA25EECF8000107147C163C4A1338A2010F147818E04A13701701011F16 C016004A14031880013F150718004A5CA2017F151E173E91C8123C177C4915FC4C5A4914 070001ED7FF0B8FCA25F38397BB838>I<0107B712FEA3903A000FF000074B1300187C02 1F153CA25DA2143FA25D1838147FA292C8FCEE03804A130718004A91C7FCA201015CA24A 131E163E010314FE91B5FC5EA2903807F800167C4A1378A2130FA24A1370A2011F14F0A2 4A90C8FCA2133FA25CA2137FA291CAFCA25BA25B487EB6FCA337397BB836>II<01 03B5D8F80FB512E0A390260007F8C7381FE0004B5DA2020F153F615DA2021F157F96C7FC 5DA2023F5D605DA2027F14016092C7FCA24A1403605CA249B7FC60A202FCC71207010315 0F605CA20107151F605CA2010F153F605CA2011F157F95C8FC5CA2013F5D5F5CA2017F14 015F91C7FC491403007FD9FE01B512F8B55BA243397CB83E>I<0103B512F8A390390007 F8005DA2140FA25DA2141FA25DA2143FA25DA2147FA292C7FCA25CA25CA21301A25CA213 03A25CA21307A25CA2130FA25CA2131FA25CA2133FA25CA2137FA291C8FC497EB6FCA25C 25397CB820>I<0103B500F890387FFFE0A21AC090260007F8C7380FFC004B15E061020F 4BC7FC183E4B5C18F0021F4A5A4D5A4BEB0F804DC8FC023F143C5F4B5B4C5A027FEB07C0 4CC9FCED001E5E4A5BED01FCECFE0315070101497E151FECFC7C4B7E903903FDE07FDAFF C07F1580ED003F49488014F84A131F83130F160F4A801607011F81A24A130383133F1601 4A80A2017F6E7EA291C8FC494A7F007F01FE011F13FCB55CA243397CB840>75 D<0107B512FCA25E9026000FF8C7FC5D5D141FA25DA2143FA25DA2147FA292C8FCA25CA2 5CA21301A25CA21303A25CA21307A25CA2130F170C4A141CA2011F153C17384A1478A201 3F157017F04A14E01601017F140317C091C71207160F49EC1F80163F4914FF0001020713 00B8FCA25E2E397BB834>I<902607FFF8923807FFF0614F13E0D9000FEFF0004F5AA202 1F167FF1EFC0141DDA1CFCEC01CF023C16DF9538039F800238ED071FA20278ED0E3F97C7 FC0270151CA202F04B5AF0707E14E0037E14E0010117FE4D485A02C0EC0380A20103ED07 01610280140EA20107ED1C0305385B14006F137049160705E05B010EEC01C0A2011E9138 03800F61011CEC0700A2013C020E131F4C5C1338ED1FB80178163F04F091C8FC01705CA2 01F04A5B187E00015DD807F816FEB500C09039007FFFFC151E150E4C397AB84A>I<9026 03FFF891B512E0A281D90007923807F8006F6E5A61020F5E81DA0E7F5DA2021E6D130703 3F92C7FC141C82DA3C1F5C70130EEC380FA202786D131E0307141C147082DAF003143C70 133814E0150101016E1378030014705C8201036E13F0604A1480163F010715C1041F5B91 C7FC17E149EC0FE360010E15F31607011E15FF95C8FC011C80A2013C805F133816001378 5F01F8157CEA03FC267FFFE0143CB51538A243397CB83E>I<0107B612F817FF1880903B 000FF0003FE04BEB0FF0EF03F8141FEF01FC5DA2023F15FEA25DA2147FEF03FC92C7FCA2 4A15F817074A15F0EF0FE01301EF1FC04AEC3F80EFFE0001034A5AEE0FF091B612C04CC7 FCD907F8C9FCA25CA2130FA25CA2131FA25CA2133FA25CA2137FA291CAFCA25BA25B1201 B512FCA337397BB838>80 DI<0103B612F017 FEEFFF80903B0007F8003FC04BEB0FF01707020FEC03F8EF01FC5DA2021F15FEA25DA214 3FEF03FC5DA2027FEC07F818F092C7120F18E04AEC1FC0EF3F004A14FEEE01F80101EC0F E091B6128004FCC7FC9138FC003F0103EC0F80834A6D7E8301071403A25C83010F14075F 5CA2011F140FA25CA2133F161F4AECE007A2017F160F180E91C7FC49020F131C007F01FE 153CB5913807F078040313F0CAEAFFE0EF3F80383B7CB83D>I<92383FC00E913901FFF0 1C020713FC91391FC07E3C91393F001F7C027CEB0FF84A130749481303495A4948EB01F0 A2495AA2011F15E091C7FCA34915C0A36E90C7FCA2806D7E14FCECFF806D13F015FE6D6D 7E6D14E0010080023F7F14079138007FFC150F15031501A21500A2167C120EA3001E15FC 5EA3003E4A5AA24B5AA2007F4A5A4B5A6D49C7FC6D133ED8F9F013FC39F8FC03F839F07F FFE0D8E01F138026C003FCC8FC2F3D7ABA2F>I<0007B812E0A25AD9F800EB001F01C049 EB07C0485AD900011403121E001C5C003C17801403123800785C00701607140700F01700 485CA2140FC792C7FC5DA2141FA25DA2143FA25DA2147FA292C9FCA25CA25CA21301A25C A21303A25CA21307A25CA2130FA25CEB3FF0007FB512F8B6FCA2333971B83B>I89 D<14F8EB07FE90381F871C90383E03FE137C EBF801120148486C5A485A120FEBC001001F5CA2EA3F801403007F5C1300A21407485C5A A2140F5D48ECC1C0A2141F15831680143F1587007C017F1300ECFF076C485B9038038F8E 391F0F079E3907FE03FC3901F000F0222677A42A>97 D<133FEA1FFFA3C67E137EA313FE 5BA312015BA312035BA31207EBE0F8EBE7FE9038EF0F80390FFC07C013F89038F003E013 E0D81FC013F0A21380A2123F1300A214075A127EA2140F12FE4814E0A2141F15C05AEC3F 80A215005C147E5C387801F8007C5B383C03E0383E07C0381E1F80D80FFEC7FCEA01F01C 3B77B926>I<147F903803FFC090380FC1E090381F0070017E13784913383901F801F838 03F003120713E0120FD81FC013F091C7FC485AA2127F90C8FCA35A5AA45AA31530153815 78007C14F0007EEB01E0003EEB03C0EC0F806CEB3E00380F81F83803FFE0C690C7FC1D26 77A426>II<147F903803FFC090380FC1E090383F00F0017E13785B485A485A485A 120F4913F8001F14F0383F8001EC07E0EC1F80397F81FF00EBFFF891C7FC90C8FC5A5AA5 5AA21530007C14381578007E14F0003EEB01E0EC03C06CEB0F806CEB3E00380781F83803 FFE0C690C7FC1D2677A426>IIIII107 DIII<147F903803FFC090380FC1F090 381F00F8017E137C5B4848137E4848133E0007143F5B120F485AA2485A157F127F90C7FC A215FF5A4814FEA2140115FC5AEC03F8A2EC07F015E0140F007C14C0007EEB1F80003EEB 3F00147E6C13F8380F83F03803FFC0C648C7FC202677A42A>I<9039078007C090391FE0 3FF090393CF0787C903938F8E03E9038787FC00170497EECFF00D9F0FE148013E05CEA01 E113C15CA2D80003143FA25CA20107147FA24A1400A2010F5C5E5C4B5A131F5EEC80035E 013F495A6E485A5E6E48C7FC017F133EEC70FC90387E3FF0EC0F8001FEC9FCA25BA21201 A25BA21203A25B1207B512C0A3293580A42A>II<3903C003F0390FF01FFC391E783C0F381C7C703A3C3EE03F8038383FC0EB7F8000 78150000701300151CD8F07E90C7FCEAE0FE5BA2120012015BA312035BA312075BA3120F 5BA3121F5BA3123F90C9FC120E212679A423>I<14FE903807FF8090380F83C090383E00 E04913F00178137001F813F00001130313F0A215E00003EB01C06DC7FC7FEBFFC06C13F8 14FE6C7F6D13807F010F13C01300143F141F140F123E127E00FE1480A348EB1F0012E06C 133E00705B6C5B381E03E06CB45AD801FEC7FC1C267AA422>II<13F8D803FEEB01C0D8078FEB03E0390E0F800712 1E121C0038140F131F007815C01270013F131F00F0130000E015805BD8007E133FA201FE 14005B5D120149137EA215FE120349EBFC0EA20201131E161C15F813E0163CD9F0031338 14070001ECF07091381EF8F03A00F83C78E090393FF03FC090390FC00F00272679A42D> I<01F0130ED803FC133FD8071EEB7F80EA0E1F121C123C0038143F49131F0070140FA25B D8F07E140000E08013FEC6485B150E12015B151E0003141C5BA2153C000714385B5DA35D A24A5A140300035C6D48C7FC0001130E3800F83CEB7FF8EB0FC0212679A426>I<01F015 07D803FC903903801F80D8071E903907C03FC0D80E1F130F121C123C0038021F131F49EC 800F00701607A249133FD8F07E168000E0ED000313FEC64849130718000001147E5B03FE 5B0003160E495BA2171E00070101141C01E05B173C1738A217781770020314F05F000301 0713016D486C485A000190391E7C07802800FC3C3E0FC7FC90393FF81FFE90390FE003F0 322679A437>I<903907E007C090391FF81FF89039787C383C9038F03E703A01E01EE0FE 3803C01F018013C0D8070014FC481480000E1570023F1300001E91C7FC121CA2C75AA214 7EA214FEA25CA21301A24A1370A2010314F016E0001C5B007E1401010714C000FEEC0380 010F1307010EEB0F0039781CF81E9038387C3C393FF03FF03907C00FC027267CA427>I< 13F0D803FCEB01C0D8071EEB03E0D80E1F1307121C123C0038140F4914C01270A249131F D8F07E148012E013FEC648133F160012015B5D0003147E5BA215FE00075C5BA214015DA3 14035D14070003130FEBF01F3901F87FE038007FF7EB1FC7EB000F5DA2141F003F5C4813 3F92C7FC147E147C007E13FC387001F8EB03E06C485A383C1F80D80FFEC8FCEA03F02336 79A428>I<903903C0038090380FF007D91FF81300496C5A017F130E9038FFFE1E9038F8 3FFC3901F007F849C65A495B1401C7485A4A5A4AC7FC141E5C5C5C495A495A495A49C8FC 131E5B49131C5B4848133C48481338491378000714F8390FF801F0391FFF07E0383E1FFF D83C0F5B00785CD8700790C7FC38F003FC38E000F021267BA422>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Ff cmbx8 8 5 /Ff 5 107 df<003FB8FCA4287FE00FFC0113800180EC007FD87E00151F007C160FA200 781607A448EE03C0A4C792C7FCB3A6013FB6FCA4322D7DAC39>84 D99 D101 D105 DI E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fg cmsy6 6 2 /Fg 2 49 df0 D48 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fh msbm8 8 3 /Fh 3 125 df<1620167016F04B5A4B5A4B5A93C7FC01FE4913042703FF801E130C48EB E03C486D5A48EBFCF0486D48131CEB01FF277C007FC0133C0078D91FE0137848D90FF813 F84890391FFE03F0021DB5FC48013C14E0DA783F13C04A6C1380902601E00713003A4003 C001FC000049C8FC130749C9FC131E5B133813102E1F7C9F37>28 D78 D124 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fi msam10 12 1 /Fi 1 4 df<007FBA1280BB12C0A300F0CB1203B3B3B3A6BBFCA36C198042447BC34D>3 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fj eufm10 12 1 /Fj 1 67 df66 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fk cmr6 6 6 /Fk 6 52 df<130C1338137013E0EA01C0EA038013005A120EA25AA25AA312781270A312 F0AB1270A312781238A37EA27EA27E7E1380EA01C0EA00E013701338130C0E317AA418> 40 D<12C012707E7E7E7E7E1380EA01C0A2EA00E0A21370A313781338A3133CAB1338A3 13781370A313E0A2EA01C0A2EA038013005A120E5A5A5A12C00E317CA418>I<1438B2B7 12FEA3C70038C7FCB227277C9F2F>43 D<13E01201120712FF12F91201B3A7487EB512C0 A212217AA01E>49 DI<13FF000313C0380F03 E0381C00F014F8003E13FC147CA2001E13FC120CC712F8A2EB01F0EB03E0EB0FC03801FF 00A2380003E0EB00F01478147C143E143F1230127812FCA2143E48137E0060137C003813 F8381E03F0380FFFC00001130018227DA01E>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fl cmmi6 6 18 /Fl 18 117 df18 D<90381FFFFC90B5FC5A4814F83907C07C00380F003C001E131C48131E12381278A2485B A35C1470007013F0495A6C485AD81C0FC7FCEA0FFEEA03F01E167E9424>27 D<127812FCA212FEA2127E1206A3120CA2121C121812301260124007107A8513>59 D<903AFFFE07FFF0A2903A07C0003E00A249485BA449C75AA4013E495AA3013FB5FC495C 90387C0003A349495AA44848495AA4484849C7FCA300075C3AFFFE07FFF0A22C227CA132 >72 D78 D<90B512FEEDFFC0903907C0 07F0ED01F890380F800016FC167CA249C712FCA316F8013E1301ED03F016E0ED0FC049EB 3F0090387FFFFC15E0017CC8FC5BA4485AA4485AA31207EAFFFEA226227CA127>80 D<001FB612FCA29039003E007C003C151C00385B12300070151812605C5AA3C648481300 A4495AA4495AA4495AA449C8FCA35B381FFFFE5C26227DA124>84 D<14E0EB01F0EB03181307130E130CEB1C30133C1338137814601370EBF0C0A2EBE18012 01EBE30013E6EA03C613CC13D813F05B12075B5BA2120F121F1237126700C31310000313 3014E0380181C0EBFF006C5A15257FA31A>96 D<131FEBFF8C3801E0DE3803807E380700 7C48133C121E123E003C5B127CA3485BA215401560903801E0C012781303393807E18039 1C1CF300380FF87F3807E03C1B177E9522>II100 D<1338137CA2137813701300A7EA0780EA1FC0EA38E01230EA60F0EA C1E0A3EA03C0A3EA0780A2EA0F0013041306EA1E0CA21318121CEA1E70EA0FE0EA07800F 237DA116>105 D<1418143C147CA214381400A7EB0780EB1FE01338EB60F013C0A2EA01 80A2380001E0A4EB03C0A4EB0780A4EB0F00A4131EA21238EA783CEAF8381378EA70F0EA 7FC0001FC7FC162D81A119>I<13F8EA0FF0A21200A2485AA4485AA43807801E147FEB81 C3EB8387380F060F495A1318EB700E4848C7FCA213FCEA1E7EEA3C0F80EB078115803978 0F0300A21402EB070600F0138CEB03F8386000F019247CA221>II<380F01F0381FC7F83831CE1CEA61F8EBF03C00C1137C13E0143838 03C000A4485AA448C7FCA4121EA2120C16177D951D>114 DI<133013785BA4 485AA4485AB51280A23803C000485AA448C7FCA4121EA25B1480383C03001306A25BEA1C 38EA0FF0EA07C011217D9F18>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fm cmex8 8 2 /Fm 2 102 df<143014FCEB03FF010F13C0013F13F090387F03F83901FC00FED807E0EB 1F80D81F80EB07E0007EC7EA01F800F0EC003C00C0150C260C80B027>98 D<017F14082601FFC0131C000701F01378489038FC01F0D83E00B512C00078013F138000 E090380FFE000040EB03F8260880AF27>101 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fn cmex10 12 21 /Fn 21 122 df0 D<12E07E12787E7E7E7F6C7E6C7E7F12016C7E7F137C137E7FA26D7EA26D7EA26D7EA36D 7EA2801301A2801300A280A2147EA2147FA4801580A7EC1FC0B3A5EC3F80A715005CA414 7EA214FEA25CA213015CA213035CA2495AA3495AA2495AA249C7FCA2137E137C13FC5B48 5A12035B485A485A90C8FC121E5A5A5A5A1A777C832E>I<16F01501ED03E0ED07C0ED0F 80ED1F005D157E5D5D14014A5A4A5A4A5AA24A5A143F92C7FC147EA25C13015C13035C13 075C130F5C131FA2495AA349C8FCA213FEA312015BA212035BA21207A25BA2120FA25BA2 121FA45BA2123FA55B127FA990C9FC5AB3AA7E7FA9123F7FA5121FA27FA4120FA27FA212 07A27FA21203A27F1201A27F1200A3137FA26D7EA36D7EA2130F80130780130380130180 1300147EA28081141F6E7EA26E7E6E7E6E7E140081157E8181ED0F80ED07C0ED03E0ED01 F0150024B26E833B>16 D<12F07E127C7E7E6C7E7F6C7E6C7E12017F6C7E137E7FA26D7E 80130F6D7EA26D7E80130180130080147E147F8081A26E7EA36E7EA26E7EA3811403A281 1401A281A21400A281A281A21680A4153FA216C0A5151F16E0A9150F16F0B3AA16E0151F A916C0153FA51680A2157FA41600A25DA25DA21401A25DA214035DA214075DA34A5AA24A 5AA34A5AA292C7FC5C147E14FE5C13015C13035C495AA2495A131F5C49C8FCA2137E5B48 5A5B1203485A485A5B48C9FC123E5A5A5A24B27C833B>I<171E173E177C17F8EE01F0EE 03E0EE07C0160FEE1F80EE3F00167E167C16FC4B5A4B5A15075E4B5A4B5A153F93C7FC5D 15FE5D14015D14034A5AA24A5AA24A5AA24A5AA24AC8FCA214FEA213015C13035C1307A2 5C130F5C131FA25C133FA3495AA349C9FCA35A5BA312035BA31207A25BA2120FA35BA312 1FA35BA3123FA55BA2127FAB485AB3B06C7EAB123FA27FA5121FA37FA3120FA37FA31207 A27FA21203A37F1201A37F7EA36D7EA36D7EA3131F80A2130F80130780A2130380130180 1300A2147FA26E7EA26E7EA26E7EA26E7EA26E7E140181140081157F8182151F6F7E6F7E 8215036F7E6F7E167C167E82EE1F80EE0FC01607EE03E0EE01F0EE00F8177C173E171E2F EE6B8349>I<12F07E127C7E7E6C7E6C7E7F6C7E6C7E6C7E137C137E7F6D7E80130F6D7E 6D7E801301806D7E147E147F80816E7EA26E7EA26E7EA26E7EA26E7EA26E7EA281818215 3F82A2151F82150F82A2150782A36F7EA36F7EA38281A31780167FA317C0A2163FA217E0 A3161FA317F0A3160FA317F8A51607A217FCABEE03FEB3B0EE07FCAB17F8A2160FA517F0 A3161FA317E0A3163FA317C0A2167FA21780A316FF1700A35D5EA34B5AA34B5AA35E150F A25E151F5E153FA25E157F93C7FC5D5DA24A5AA24A5AA24A5AA24A5AA24A5AA24A5A92C8 FC5C147E14FE495A5C13035C495A495A131F5C49C9FC137E137C13FC485A485A485A5B48 5A48CAFC123E5A5A5A2FEE7C8349>I[51 298 104 131 79 32 D[<12F87E127E7E7F121F6C7E6C7E7F6C7E12016C7E7F137F7F806D7E6D7EA26D7E80 13036D7EA26D7E808081143F81141F816E7EA26E7EA26E7EA26E7EA36E7EA26F7EA28215 3FA282151F82150FA2821507A282150382A3150182A28183A3707EA4707EA483161FA483 160FA383A31607A383A31603A383A582A21880A882A218C0AD177F18E0B3B3A618C017FF AD1880A25EA81800A25EA55FA31607A35FA3160FA35FA3161F5FA4163F5FA44C5AA44C5A A394C7FC5DA25E1503A35E15075EA2150F5EA2151F5E153F5EA2157F5EA24BC8FCA24A5A A34A5AA24A5AA24A5AA24A5A5D143F5D147F92C9FC5C5C495AA2495A13075C495AA2495A 495A91CAFC5B13FE5B485A1203485A5B485A485A123F90CBFC127E5A5A>51 298 125 131 79 I56 D58 D<913807FF80B3B3B04A1300A55D141FA35D143F5DA2147F5D14FF5D A2495B5D5B4990C7FC5C130F5C495A495A495AA2495A485B4890C8FCEA07FC485A485AEA 7FE0EAFF8090C9FC12FCB4FC7FEA7FE0EA1FF06C7E6C7E6CB4FC6C7F6C7F6D7EA26D7E6D 7E6D7E801307806D7F7F816D7FA281147F81143FA281141F81A3140F81A56E1380B3B3B0 21B56F8059>60 D<12F0B3B3B3A8043E618042>63 D<94381FFF800403B512FC043FECFF C093B712F0030716FE031F707E037F17E04AB5D8F1FC14F84AD9FE0101077F4A01F00200 7F021F018092381FFF8091263FFE0003077FDA7FF804017FDAFFE0706C7E4949717E4949 717E4948C7EE07FE4948727E4948727F4948727F4A197F4948737E4948737E91C8170F48 48747E000388491A034848747EA24848747EA24848F37F80A2491B3F003F1DC0A2491B1F 007F1DE0A290C9180FA3481DF0A2481C07A2BFFCA748C9D801FCC91207A36C1C0FA26C1D E0A36D1B1FA2003F1DC06D1B3FA2001F1D806D1B7FA26C6CF3FF00A26C6C505AA26C6C50 5A6D1A070001646C6C505A6E191F6D6C4F5A6D6C4F5A6E19FF6D6C4E5B6D6C4E90C7FC6D 6C4E5A6D6C6CEF1FFC6D6D4D5A6D6D4D5ADA7FF84C485ADA3FFE04075B91261FFF80031F 5B020701F0DBFFFEC8FC6E01FE02075B6ED9FFF190B55A6E6C90B712E0031F178003074C C9FC030016F0043F15C0040302FCCAFCDC001F138064647B7F6F>76 D<963807FFF84EB612E0061F15FE95B812C0050717F8053F17FF94BA12C0040319F0040F 19FC043F9126FC7FCF14FF4C0200D9C03F804BB500F0030314E04B0280DB007F7F030F01 FCC7030F13FC4B01F005037F4B01C005007F92B5C8043F13C04A01FC070F7F4A49737F4A 01E007017F4A49737F4A49747E4A48C9EF1FFF4A48757F4A48757F4949757F4B87494975 7F4949767E4990CA727E4A1D1F4948777EA24948777E4948777F4A8901FF8C4A89488D4A 1E7F4890CB737EA24848797EA2491F0F000F8D491F07A2001F8D491F03A2003F8D498BA3 007F2280498BA500FF22C049207FA390C3FCA90180CBD87FC0CB127FA36D20FF007F2280 A56D67003F2200A36D67001F69A26D1F07000F69A26D1F0F0007696D1F1FA26C6C555AA2 6C6D545A6E1EFF6C696E65017F686E656D6C5390C7FC6D6C535AA26D6C535A6E1D3F6D6D 525A6D6D525A6D6D515B6F636D6D515B6E6C515B6E6C5190C8FC6E6C6CF27FFE6E6D505A 6E6D4F5B6E01F807075B6E6D4F5B6E01FF073F5B033F01C095B5C9FC6F01F005035B6F01 FC050F5B0303D9FF80047F13F06F02F00303B55A6F6C01FF033F14807002FC01CFB6CAFC 040F91B812FC040319F0040019C0053F95CBFC050717F8050017C0061F4BCCFC060115E0 DE000701F8CDFC8A8B7A7F97>I81 D<007C193EA200FE197FB3B3B3AE6C19FFA26C19FEA26D1701A26C 6CEF03FCA2001F19F86D17076D170F000F19F06C6CEF1FE06D173F6C6CEF7FC06C6CEFFF 806E5D6C01E0030713006D6C4B5AD93FFCED3FFC6DB4EDFFF86D01E001075B6D01FE017F 5B010190B712806D94C7FC023F15FC020F15F002011580DA003F01FCC8FC030313C04864 7B7F53>83 D88 D I<153015FC4A7E913807FF80021F13E0027F13F89138FFCFFC0103EB03FF90260FFC0013 C0D93FF0EB3FF0D97FC0EB0FF84848C7EA03FED807F89138007F80D81FE0ED1FE0D87F80 ED07F800FEC9EA01FC00F8EE007C00E0171C361280C937>98 D101 D<140FB3B3A200C0163000F016F000FC1503B4150FD83FC0EC3FC0D80FE0EC7F00D803F8 EB01FCD800FCEB03F0017E495A011FEB0F8090260FCF3FC7FC903807EF7E6DB45A6D5B6D 5B6E5A6E5A6E5A6EC8FCA214062C3B757F42>121 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fo msbm10 12 8 /Fo 8 125 df<1840EF01E017031707604D5A171F4DC8FC177ED90FF84A14C0D93FFF49 48130190B538C003F04802E05B489138F807C048ECFC0F486E48481303281FF80FFF3FC7 FCD9E00113FE283F80007FFCEC078090C76C5A007E020F150F007C6E6C141F007803FFEC 3F004B6D5B484A9038E001FE92393F3FFC07DB7E1FB55A484A6C5C4B6C5C912601F0015C 02036D5C4A48013F90C7FC00604948EB07FCC7484890C9FC4ACBFC147E147C5C13015C5C EB0080422A7BAD4D>28 D<18074E7EA24EC7FCA2183EA2D90FFC4B1380D97FFF9238FC01 C090B500C014F8000302F0EB01F04814FC486EEB03E0281FF003FF801403D980009026C0 07C0138048C7263FF00F1307003CDA0FF8EB800F48913B03FE1F001F00922601FF9F5B00 70913A007FFE01FE00F0033FEB0FFC48030FB55A705C04015C614EC7FC0040923803E1F0 C901E0C8FC4C5A160F5F4CC9FCA2163EA25E16FC5E4B5AA24B5AA2BB12C0A36C1980C800 1FCAFC153EA25D15FC5D4A5AA24A5AA24A5A140F5D4ACBFCA2143EBB12C0A36C19802600 01F0CBFCA2495AA2495A130F5C49CCFCA2133EA25BA2133842507BC04D>I<922601FFE0 1330033F01FC13784AB6FC020FEDC0F8023F9038C07FF8913AFFFE000FFF4901F8130390 2607FBF07F90260FE7E0EB007F90261F87C0EC3F78494848141FD97E1FED0FF801FC90C8 FC2601F83E1507D803F0160348485A01C01601380F807802F81500EA1F004A1678EA3E01 A2003C5B007C183019001278130312F85C12F0AC12F8A200787FA2EA7C01A2123C003E7F A2EA1F00A26C6C7E19062607C07C160F01E0171F6C6C6C163FD801F8177E6C6C6C167C01 7E6D15FCD93F0FED01F890261F87C0EC07F090260FE7E0EC0FE0902607FBF8EC3FC09026 01FFFE903801FF806D903AFFC00FFE00023F90B55A020F15F0020115C0DA003F49C7FC03 0113F040487CC52E>67 D<007FB54AB512C0B66C4914E0816C6E6D14C02707F003F09039 000FF8002601F801ED03F000006D7E017C6D6E5A017E137E017F133E8102807FECC00F6E 6C7E017B80903979F003F0ECF801903978FC00F8027C7F6E137E023F133E6E6C7E020F14 80913907C00FC0EDE007913903F003E0020114F0913900F801F8EDFC00037E137C033E13 7E6F133EEE801FDB0FC013810307EB0FC1923803E0079338F003E1DB01F813F1923900FC 01F9EE7C0070137D043F137F93381F803F040F131F933807C00F17E0933803F007040113 03933800F80117FC177E173E171F1881EF0FC11707EF03E118F1EF01F91700187D01FC16 7F183FD803FF161F007F01F8150FB57E18076C491503CB1201725A43467DC339>78 D<923807FFC092B512FE0207ECFFC0021F15F0027F010113FC903B01FFF8003FFF4901E0 010F7F010F496D13E090261FCF80903803E7F0D93F1FC73801F1F8017EEEF0FCD9FC3E91 3800F87ED801F88348484892387C1F8001E0170F48484892383E07C0000F19E04948ED1E 03D81F00EF01F00101161F001E1800003E496F13F8A2003C1978007C197C010317800078 193C4A150700F8193EA200F0191EAC00F8193EA20078193C6E150F007C197C0101170000 3C1978003E19F8A2001E6D4B13F0001F18010100161ED80F80EF03E06D6CED3E07000719 C02603E07C92387C0F8001F0171F6C6C6C9238F83F00D800FC177ED97E1F4A485A013FEE F1F890261FCF80903803E7F06DB46C49B45A01036D4913806D01F8013F90C7FC903B007F FF01FFFC021F90B512F0020715C002004AC8FC6F5B92387C007C6F7F173F6F6D7E706C7E 92390FC007F00307EB03FC923B03F000FF80707090387FFFF8DB00FC131F047F010713F0 93263FC00013E093260FFC0113C070B61200040114FC706C13F0050790C7FC47597DC53C >81 D83 D<0003B812FE4883A301879039000F803ED98F F0011F137ED9BFC0EC007C01FFC7003E5B13FC48484A485A49ECFC034902F85B4B48485A 5B494948485A0307131F04C090C7FC90C7380F803EA24B485A00064A13FCC8003E5B4B48 5AA24B485A0201130703F05B4A48485AA24A4848C8FC5E91380F803E021F5B1500023E5B 1501027C5B9138FC03E014F84948485AA24948485A0107011F156002C090C812F090380F 803EA249484814014913FC013E5B494848EC03E0A249484814070001130701F049140F48 484848141FA2484848C8EA3FC0000F49157FD9803E15FF484848EC01FBEF07F3003E49EC 0FE7D87E01ED7F87007C49903903FF0780BAFCA36C18003C447DC345>90 D<387FFFC0B57EA27EEA1F01EA0F81A21207AF030FB5FC4B1480A26F1400923803E7F892 3801EFE0EEFF8094C7FC16FC4B5A5E4B5A4B5A4B5A4BC8FC157E5D14E1ECE7FEECEFFFEC FF9FED0F8002FE7F6E6C7E1503ED81F09138EFC1F89138E7E0FC02E3137C9138E1F03EED F83F02E06D7EED7C0F92387E07C0033F7FED1F0392380F81F0EEC1F8923807C0FC000F90 39F003E07C83271F00F801133F277FFFFE0FB512C0B64814E0A26C496C14C033447EC346 >124 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fp cmr9 9 35 /Fp 35 128 df<137813FCA212011203EA07F813E0EA0FC0EA1F801300123C5A5A12400E 0E71B326>19 D45 D48 D<13075B5B137FEA07FFB5FC13BFEAF83F1200B3B3A2497E007FB5 1280A319327AB126>IIII<000C14C0380FC00F90B5128015005C5C14F014C0 D80C18C7FC90C8FCA9EB0FC0EB7FF8EBF07C380FC03F9038001F80EC0FC0120E000CEB07 E0A2C713F01403A215F8A41218127E12FEA315F0140712F8006014E01270EC0FC06C131F 003C14806CEB7F00380F80FE3807FFF8000113E038003F801D347CB126>I<14FE903807 FF80011F13E090383F00F0017C13703901F801F8EBF003EA03E01207EA0FC0EC01F04848 C7FCA248C8FCA35A127EEB07F0EB1FFC38FE381F9038700F809038E007C039FFC003E001 8013F0EC01F8130015FC1400A24814FEA5127EA4127F6C14FCA26C1301018013F8000F14 F0EBC0030007EB07E03903E00FC03901F81F806CB51200EB3FFCEB0FE01F347DB126>I< 1230123C003FB6FCA34814FEA215FC0070C7123800601430157015E04814C01401EC0380 C7EA07001406140E5C141814385CA25CA2495A1303A3495AA2130FA3131F91C7FCA25BA5 5BA9131C20347CB126>III<15E0A34A7EA24A7EA34A7EA3EC0DFE140CA2EC187FA34A6C7E A202707FEC601FA202E07FECC00FA2D901807F1507A249486C7EA301066D7EA2010E8001 0FB5FCA249800118C77EA24981163FA2496E7EA3496E7EA20001821607487ED81FF04A7E D8FFFE49B512E0A333367DB53A>65 D67 DIIIIII<01 7FB5FCA39038003FE0EC1FC0B3B1127EB4FCA4EC3F805A0060140000705B6C13FE6C485A 380F03F03803FFC0C690C7FC20357DB227>II< B512FEA3D803FEC9FC6C5AB3A9EE0180A416031700A45EA25E5E5E5E16FE00031407B7FC A329337DB230>IIIIIII<90381FE00390387FFC0748 B5FC3907F01FCF390F8003FF48C7FC003E80814880A200788000F880A46C80A27E92C7FC 127F13C0EA3FF013FF6C13F06C13FF6C14C06C14F0C680013F7F01037F9038003FFF1403 02001380157F153FED1FC0150F12C0A21507A37EA26CEC0F80A26C15006C5C6C143E6C14 7E01C05B39F1FC03F800E0B512E0011F138026C003FEC7FC22377CB42B>I<007FB712FE A390398007F001D87C00EC003E0078161E0070160EA20060160600E01607A3481603A6C7 1500B3AB4A7E011FB512FCA330337DB237>II87 D<003FB612FCA39039F80007F813C090C7EA0FF000 3EEC1FE0123C0038EC3FC00078EC7F801270EDFF004A5AA20060495AA24A5A4A5AC7FC4A 5A4A5AA24A5A4AC7FCA2495A495AA2495A495AA24948130C495AA2495A49C7FCA2484814 1CA2485A485A1638485A4848147816F84848130148481307153FB7FCA326337CB22F>90 D<001C1370387F01FC00FF13FEA4007F13FC381C0070170879B226>127 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fq cmsy10 10 1 /Fq 1 25 df24 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fr cmtt10 10 23 /Fr 23 123 df<007FB6FCB71280A46C150021067B9B2C>45 D<121FEA3F80EA7FC0EAFF E0A5EA7FC0EA3F80EA1F000B0B708A2C>I<1507ED0F80151FA2153F16005D157E15FE5D 14015D14035DA214075D140F5D141F5D143F92C7FC5C147E14FE5CA213015C13035C1307 5C130F5C131F5CA2133F91C8FC5B137E13FE5B12015B12035B12075BA2120F5B121F5B12 3F90C9FC5A127E12FE5AA25A127821417BB92C>I64 D<007FB512C0B612F88115FF6C15802603F00013C0153FED0FE0ED07F0A2150316F81501 A6150316F01507A2ED0FE0ED3FC015FF90B61280160015FC5D15C001F0C8FCB0387FFF80 B57EA36C5B25337EB22C>80 D<3801FFF0000713FE001F6D7E15E048809038C01FF81407 EC01FC381F80000006C77EC8127EA3ECFFFE131F90B5FC1203120F48EB807E383FF800EA 7FC090C7FC12FE5AA47E007F14FEEB8003383FE01F6CB612FC6C15FE6C14BF0001EBFE1F 3A003FF007FC27247CA32C>97 DI<903803FFE0011F13F8017F13FE48B5FC488048 48C6FCEA0FF0485A49137E4848131890C9FC5A127EA25AA8127EA2127F6C140F6DEB1F80 6C7E6D133F6C6CEB7F003907FE03FF6CB55A6C5C6C6C5B011F13E0010390C7FC21247AA3 2C>III104 D<1307EB1FC0A2497EA36D5AA20107C7FC90C8FCA7387FFFC080B5FC7EA2 EA0007B3A8007FB512FCB612FEA36C14FC1F3479B32C>I107 D<387FFFE0B57EA37EEA 0003B3B3A5007FB61280B712C0A36C158022337BB22C>I<3A7F83F007E09039CFFC1FF8 3AFFDFFE3FFCD87FFF13FF91B57E3A07FE1FFC3E01FCEBF83F496C487E01F013E001E013 C0A301C01380B33B7FFC3FF87FF0027F13FFD8FFFE6D13F8D87FFC4913F0023F137F2D24 81A32C>I<397FF01FE039FFF87FFC9038F9FFFE01FB7F6CB6FC00019038F03F80ECC01F 02807FEC000F5B5BA25BB3267FFFE0B5FCB500F11480A36C01E0140029247FA32C>II114 D<90387FF8700003B512F8120F5A5A387FC00F387E00034813015AA36CEB00F0007F1400 13F0383FFFC06C13FE6CEBFF80000314E0C66C13F8010113FCEB0007EC00FE0078147F00 FC143F151F7EA26C143F6D133E6D13FE9038F007FC90B5FC15F815E000F8148039701FFC 0020247AA32C>I<131E133FA9007FB6FCB71280A36C1500D8003FC8FCB1ED03C0ED07E0 A5EC800F011FEB1FC0ECE07F6DB51280160001035B6D13F89038003FE0232E7EAD2C>I< 3A7FF003FF80486C487FA3007F7F0001EB000FB3A3151FA2153F6D137F3900FE03FF90B7 FC6D15807F6D13CF902603FE07130029247FA32C>I119 D<003FB612E04815F0A4007EC7EA1FE0ED3FC0ED7F80EDFF004A5A00 3C495AC7485A4A5A4A5A4A5A4A5A4AC7FCEB01FC495AEB0FF0495A495A495A49C8FC4848 EB01E04848EB03F0485A485A485A485A485AB7FCA46C15E024247DA32C>122 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fs cmti12 12 56 /Fs 56 123 df12 D<167016E0ED01C0ED0380ED0700150E153C5D15F85D4A5A4A5A4A5A140F4AC7FC141E14 3E5C147814F8495A5C1303495AA2495AA249C8FCA25B133E137E137CA25BA212015BA212 035BA212075BA2120FA25BA2121FA290C9FCA25AA2123EA3127EA2127CA65AAB1278A612 7C123CA47EA2120E120FA27E6C7EA26C7EA26C7E1360246472CA28>40 D<1560A2157081A281151E150E150FA2811680A3ED03C0A516E0A21501A71503A91507A2 16C0A4150FA21680A2151FA21600A25DA2153EA2157EA2157C15FCA25D1401A25D14035D A214075D140F5DA24AC7FCA2143EA25C147814F8495AA2495A5C1307495A91C8FC131E13 3E5B13785B485A485A485A48C9FC121E5A5A12E05A23647FCA28>I<13F0EA03FC1207A2 EA0FFEA4EA07FCEA03CCEA000C131C1318A2133813301370136013E0EA01C013801203EA 0700120E5A5A5A5A5A0F1D7A891E>44 D<007FB5FCB6FCA214FEA21805789723>I<120F EA3FC0127FA212FFA31380EA7F00123C0A0A76891E>I<16C01501A215031507ED0F8015 1F153F157F913801FF005C140F147F903807FCFEEB0FF0EB0700EB00015DA314035DA314 075DA3140F5DA3141F5DA3143F5DA3147F92C7FCA35C5CA313015CA313035CA313075CA2 130FA2131F133FB612FCA25D224276C132>49 DI52 D<130FEB1FC0133FEB7FE013FFA214C0EB7F801400131E90C7FCB3A5120FEA3FC012 7FA212FFA35B6CC7FC123C132B76AA1E>58 D<14F0EB01FC1303EB07FE130FA214FCEB07 F814F0EB01E090C7FCB3A513F0EA03F8487EA2120FA46C5AEA03D8EA001813381330A213 70136013E05B12015B120348C7FC1206120E5A5A5A5A5A173E7AAA1E>I65 D<91B712FCF0FF8019E00201903980001FF06E90C7EA07F84A6F7E727E4B81841A800203 167F5DA314075D19FFA2020F17004B5C611803021F5E4B4A5A180F4E5A023F4B5A4BEC7F 804EC7FCEF03FC027FEC0FF84BEBFFC092B6C8FC18E0913AFF800007F892C7EA01FC717E 187F49834A6F7EA30103835CA313075CA3010F5F4A157FA24E5A131F4A4A90C7FC601703 013F4B5A4A4A5A4D5A017F4B5A4D5A4A4948C8FC01FFEC0FFEB812F817C04CC9FC41447A C345>II<91 B712F818FF19C00201903980003FF06E90C7EA0FF84AED03FCF000FE4B157FA2F13F8002 03EE1FC05DF10FE0A214074B16F01907A2140F5D1AF8A2141F5DA2190F143F5D1AF0A214 7F4B151FA302FF17E092C9123FA34918C04A167F1A80A2010317FF4A1700A24E5A13074A 4B5A611807010F5F4A4B5A181F61011F4C5A4A4BC7FC18FE4D5A013F4B5A4A4A5A4D5A01 7FED3FC005FFC8FC4AEB03FE01FFEC1FF8B812E094C9FC16F845447AC34A>I<91B91280 A30201902680000713006E90C8FC4A163FA24B81A30203160E5DA314074B151E191CA214 0F5D17075F021F020E90C7FC5DA2171E023F141C4B133CA2177C027F5CED800392B5FCA2 91B65AED00071601A2496E5A5CA2160101035D5CA2160301075D4A90CAFCA3130F5CA313 1F5CA3133F5CA2137FA313FFB612E0A341447AC340>70 DI<91B6D8803FB512E0A302010180C7 387FE0006E90C86C5A4A167FA24B5EA219FF14034B93C7FCA26014074B5DA21803140F4B 5DA21807141F4B5DA2180F143F4B5DA2181F147F92B75AA3DAFF80C7123F92C85BA2187F 5B4A5EA218FF13034A93C8FCA25F13074A5DA21703130F4A5DA21707131F4A5DA2170F13 3F4A5DA2017F151FA24A5D496C4A7EB6D8803FB512E0A34B447AC348>I<027FB512E091 B6FCA20200EBE000ED7F8015FFA293C7FCA35C5DA314035DA314075DA3140F5DA3141F5D A3143F5DA3147F5DA314FF92C8FCA35B5CA313035CA313075CA3130F5CA3131F5CA2133F A25CEBFFE0B612E0A25D2B447BC326>I<031FB512F05DA29239000FFC005FA35FA2161F A25FA2163FA25FA2167FA25FA216FFA294C7FCA25DA25EA21503A25EA21507A25EA2150F A25EA2151FA25EA2153FA25EA2157FA25EEA0F80D83FE013FF93C8FC127FA24A5AEAFFC0 4A5A1300007C495A0070495A4A5A6C5C003C495A6C01FEC9FC380F81F83803FFE0C690CA FC344679C333>I<91B66C90383FFFF8A302010180C7000F13006E90C8EA07FC4A17F01A C04B4B5A4FC7FC193C02035E4B5DF003E0F0078002074BC8FC4B141E6018F8020F4A5A4B EB03C04D5A4DC9FC021F141E4B137C17F04C5A023F495A4B487E161F163F027F497EED80 FFED81EF923883CFF89138FF8F8FED1E07033C7F157849EBF00303E07F15C092380001FF 495A5C707FA213074A6E7EA2173F010F825C171F84131F4A140F84A2013F6F7E5CA2017F 6F7EA24A4A7E496C4A7FB66C90B512FC5E614D447AC34B>I<91B612F0A25F020101C0C7 FC6E5B4A90C8FCA25DA314035DA314075DA3140F5DA3141F5DA3143F5DA3147F5DA314FF 92C9FCA35B5CA3010316104A1538A21878010716705C18F018E0010F15015C18C0170301 1F15074A1580170FA2013FED1F004A5C5F017F15FE16034A130F01FFEC7FFCB8FCA25F35 447AC33D>I<91B56C93387FFFC08298B5FC02014DEBC0006E614A5FA203DF4C6CC7FC1A 0E63912603CFE05D038F5F1A381A711407030FEEE1FCA2F101C3020FEE0383020E60F107 036F6C1507021E160E021C60191CF1380F143C023804705BA2F1E01F0278ED01C0912670 03F85EF003801A3F02F0ED070002E0030E5CA24E137F130102C04B91C8FC606201036D6C 5B02805F4D5A943803800113070200DA07005BA2050E1303495D010E606F6C5A1907011E 5D011C4B5CA27048130F133C01384B5C017892C7FC191F01F85C486C027E5DD807FE027C 4A7EB500F00178013FB512C0A216705A447AC357>I<91B56C49B512E0A2820200923900 0FFC00F107F0706E5A4A5F15DF705D1907EC03CFDB8FF892C7FCA203875D02077F030315 0EA270141EEC0F01020E161C826F153C141E021C6E1338167F1978023C800238013F1470 A27113F00278131F02705E83040F130102F014F84A5E1607EFFC0313014A01035C17FE18 07010314014A02FF90C8FCA2705B0107168F91C8138E177F18DE5B010EED3FDC18FCA201 1E151F011C5EA2170F133C01386F5A1378A201F81503486C5EEA07FEB500F01401A2604B 447AC348>I<91B712F018FEF0FF800201903980007FE06E90C7EA1FF04AED07F818034B 15FCF001FE1403A24B15FFA21407A25DA2140FF003FE5DA2021F16FC18074B15F8180F02 3F16F0F01FE04B15C0F03F80027FED7F0018FE4BEB03FCEF0FF002FFEC7FC092B6C7FC17 F892CAFC5BA25CA21303A25CA21307A25CA2130FA25CA2131FA25CA2133FA25CA2137FA2 5C497EB67EA340447AC342>80 D83 D<48B912F85AA2913B0007FC001FF0D807F84A130701E0010F140349160148485C90 C71500A2001E021F15E05E121C123C0038143F4C1301007818C0127000F0147F485DA3C8 00FF91C7FC93C9FCA35C5DA314035DA314075DA3140F5DA3141F5DA3143F5DA3147F5DA3 14FF92CAFCA35B5CA21303A21307497E007FB612C0A25E3D446FC346>I86 DI<007FB54AB51280B65CA2000101E091 39007FF0006C49ED3FC04A93C7FC6D6C153E601878013F5E6E4A5A604D5A6D6C4AC8FC5F 171E010F151C6E5C5F010715F06E495A5F4C5A6D6C49C9FC5E161E0101141C6E5B5E16F0 6DEB81E05EED8380DA7F87CAFC15CF15DEEC3FDC15F85DA26E5A5D143FA35D147FA392CB FC5CA35C1301A35C1303A3495AA3497E000FB512F8A341446DC348>89 D97 DIIIII<15FCEC03FF91390F838380 91393E01CFC091387C00EF4A13FF4948137F010315804948133F495A131F4A1400133F91 C75A5B167E13FE16FE1201495CA215011203495CA21503A2495CA21507A25EA2150F151F 5E0001143F157F6C6C13FF913801DF8090387C039F90383E0F3FEB0FFCD903F090C7FC90 C7FC5DA2157EA215FEA25DA2001C495A127F48495A14074A5A485C023FC8FC00F8137E38 7C01F8381FFFE0000390C9FC2A407BAB2D>I<14FE137FA3EB01FC13001301A25CA21303 A25CA21307A25CA2130FA25CA2131FA25C157F90393F83FFC091388F81F091381E00F802 387F4948137C5C4A137EA2495A91C7FCA25B484814FE5E5BA2000314015E5BA200071403 5E5B1507000F5DA249130F5E001F1678031F1370491480A2003F023F13F0EE00E090C7FC 160148023E13C01603007E1680EE070000FEEC1E0FED1F1E48EC0FF80038EC03E02D467A C432>I<143C147E14FE1301A3EB00FC14701400AE137C48B4FC3803C780380703C0000F 13E0120E121C13071238A21278EA700F14C0131F00F0138012E0EA003F1400A25B137EA2 13FE5B12015BA212035B141E0007131C13E0A2000F133CEBC038A21478EB807014F014E0 EB81C0EA0783EBC7803803FE00EA00F8174378C11E>I<16F0ED03F8A21507A316F0ED01 C092C7FCAEEC01F0EC07FCEC1E1EEC380F0270138014E0130114C0EB03800107131F1400 A2130E153F131E011C140090C7FC5DA2157EA215FEA25DA21401A25DA21403A25DA21407 A25DA2140FA25DA2141FA25DA2143FA292C7FCA25C147EA214FE001C5B127F48485A495A A248485A495AD8F81FC8FCEA707EEA3FF8EA0FC0255683C11E>I<14FE137FA3EB01FC13 001301A25CA21303A25CA21307A25CA2130FA25CA2131FA25C167E013F49B4FC92380783 C09138000E07ED3C1F491370ED603F017E13E0EC01C09026FE03801380913907000E00D9 FC0E90C7FC5C00015B5C495AEBF9C03803FB8001FFC9FCA214F03807F3FCEBF07F9038E0 1FC06E7E000F130781EBC003A2001F150FA20180140EA2003F151E161C010013E0A2485D A2007E1578167000FE01015B15F1489038007F800038021FC7FC2A467AC42D>IIIIII<91381F800C91387FE01C903901F0703C903907C0387890390F801CF890 381F001D013E130F017E14F05B48481307A2484814E012075B000F140F16C0485AA2003F 141F491480A3007F143F90C71300A35D00FE147EA315FE5DA2007E1301A24A5A1407003E 130FA26C495A143B380F80F33807C3E73901FF87E038007E071300140F5DA3141F5DA314 3F92C7FCA25CA25C017F13FEA25D263F76AB2D>III<1470EB01F8A313035CA313075CA3130F5CA3131F5CA2 007FB512E0B6FC15C0D8003FC7FCA25B137EA313FE5BA312015BA312035BA312075BA312 0F5BA2EC0780001F140013805C140E003F131EEB001C143C14385C6C13F0495A6C485AEB 8780D807FEC7FCEA01F81B3F78BD20>I<137C48B414072603C780EB1F80380703C0000F 7F000E153F121C0107150012385E1278D8700F147E5C011F14FE00F05B00E05DEA003FEC 0001A2495C137E150313FE495CA215071201495CA2030F13380003167849ECC070A3031F 13F0EE80E0153F00011581037F13C06DEBEF8300000101148090397C03C787903A3E0F07 C70090391FFE01FE903903F000782D2D78AB34>I<017C143848B414FC3A03C78001FE38 0703C0000F13E0120E001C14000107147E1238163E1278D8700F141E5C131F00F049131C 12E0EA003F91C7123C16385B137E167801FE14705BA216F0000115E05B150116C0A24848 EB0380A2ED0700A2150E12015D6D5B000014786D5B90387C01E090383F0780D90FFFC7FC EB03F8272D78AB2D>I<017CEE038048B4020EEB0FC02603C780013FEB1FE0380703C000 0E7F5E001C037E130F01071607123804FE130300785DEA700F4A1501011F130100F00180 4914C012E0EA003FDA000314034C14805B137E0307140701FE1700495CA2030F5C000117 0E495CA260A24848495A60A2601201033F5C7F4B6C485A000002F713036D9039E7E00780 90267E01C349C7FC903A1F0781F81E903A0FFF007FF8D901FCEB0FE03B2D78AB41>I<02 F8133FD907FEEBFFE0903A0F0F83C0F0903A1C07C780F890393803CF03017013EE01E0EB FC07120101C013F8000316F00180EC01C000074AC7FC13001407485C120EC7FC140F5DA3 141F5DA3143F92C8FCA34AEB03C01780147EA202FEEB0700121E003F5D267F81FC130E6E 5BD8FF83143CD903BE5B26FE079E5B3A7C0F1F01E03A3C1E0F83C0271FF803FFC7FC3907 E000FC2D2D7CAB2D>I<137C48B414072603C780EB1F80380703C0000F7F000E153F001C 1600130712385E0078157EEA700F5C011F14FE00F0495B12E0EA003FEC00015E5B137E15 0301FE5C5BA2150700015D5BA2150F00035D5BA2151F5EA2153F12014BC7FC6D5B00005B EB7C0390383E0F7EEB1FFEEB03F090C712FE5DA214015D121F397F8003F0A24A5A484848 5A5D48131F00F049C8FC0070137E007813F8383801F0381E07C06CB4C9FCEA01FC294078 AB2F>I<027C130749B4130F49EB800E010F141E49EBC03CEDE03890393F03F07890397C 00FDF00178EB3FE00170EB03C001F0148049130790C7EA0F00151E5D5D5D4A5A4A5A4A5A 4AC7FC141E5C5C5C495A495A495A49C8FC011E14F04914E05B491301485A4848EB03C0D8 07B0130701FEEB0F80390FCF801F3A1F07E07F00393E03FFFED83C015B486C5B00705C00 F0EB7FC048011FC7FC282D7BAB28>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Ft cmr8 8 13 /Ft 13 112 df0 D<156015F0A24A7E4A7EA24A7E1406EC0E7F14 0C91381C3F8014184A6C7E150F02607F150702C07F1503D901807F1501D903007F496D7E 1306010E147F130C011C6E7E131801386E7E1330496E7E160749811603484881160148C8 7F486F7E1206000E167F120C001CEE3F801218003FB812C0A24817E0A2B912F0342F7DAE 3B>I<913901C001C0A30203130303805BA302071307030090C7FCA34A5B020E130EA302 1E131E021C131CA3023C133CB912C0A3C726700070C7FC02F013F04A5BA40101130102C0 5BA40103130302805BB912C0A327000F000FC8FC010E130EA3011E131E011C131CA3013C 133C01381338A30178137801701370A301F013F0495BA3323B7CAD3B>35 D<13031307130E131C1338137013F0EA01E013C01203EA0780A2EA0F00A2121EA35AA45A A512F8A25AAB7EA21278A57EA47EA37EA2EA0780A2EA03C0120113E0EA00F01370133813 1C130E1307130310437AB11B>40 D<12C07E12707E7E7E120FEA0780120313C0EA01E0A2 EA00F0A21378A3133CA4131EA5131FA2130FAB131FA2131EA5133CA41378A313F0A2EA01 E0A2EA03C013801207EA0F00120E5A5A5A5A5A10437CB11B>I43 D48 D<130C133C137CEA03FC12FFEAFC7C1200B3B113FE387FFFFEA2172C7AAB23>III61 D99 D111 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fu cmsy8 8 15 /Fu 15 107 df0 D<123C127E12FFA4127E123C08087A9414>I< 006015C000E014016C14030078EC07806CEC0F006C141E6C5C6C6C5B6C6C5B6C6C485A6C 6C485A90387807806D48C7FCEB1E1E6D5AEB07F86D5A6D5A497E497EEB0F3CEB1E1E497E 496C7E496C7E48486C7E48486C7E4848137848C77E001E80488048EC078048EC03C04814 0100601400222376A137>I<140381B3A3B812FCA3C7D80380C7FCB3B812FCA32E2F7CAD 37>6 DI< EC3FF0903801FFFE903907C00F8090391E0001E00178EB007801E0141C48488048488048 6CEC0F80D80EE0EC1DC0D80C701438D81C38EC70E0D8181CECE060D8380E903801C070D8 300790380380303B700380070038276001C00E13186D6C5A00E0D97038131C486D48130C 6E5AEC0FC06E5A6EC7FC4A7E4A7EEC1CE0EC38706C496C131C0060496C131849487E2770 03800713383B300700038030D8380E903801C070D8181C903800E060D81C38EC70E0D80C 70EC38C0D80EE0141D6C48EC0F806C48EC07006C6C140E6C6C5C01781478011EEB01E090 3907C00F80902601FFFEC7FC9038003FF02E2F7CA737>10 D20 D<12E012F812FEEA3F80 EA0FE0EA03F8EA00FEEB3F80EB0FE0EB03F8EB00FC143FEC0FC0EC07F0EC01FCEC007FED 1FC0ED07F0ED01FCED007FEE1FC01607161FEE7F00ED01FCED07F0ED1FC0037FC7FCEC01 FCEC07F0EC0FC0023FC8FC14FCEB03F8EB0FE0EB3F8001FEC9FCEA03F8EA0FE0EA3F8000 7ECAFC12F812E0CBFCAD007FB71280B812C0A22A3B7AAB37>I<01FE150C3803FF804813 E0487F381F83F8263E00FC141C003C133F486D6C131800706D6C133800606D6C137800E0 D901F013F0913800FC014891387F07E092383FFFC06F138003071300ED01FC2E117C9837 >24 D<137813FE1201A3120313FCA3EA07F8A313F0A2EA0FE0A313C0121F1380A3EA3F00 A3123E127E127CA35AA35A0F227EA413>48 D<91B512C01307131FD97F80C7FC01FCC8FC EA01F0EA03C0485A48C9FC120E121E5A123812781270A212F05AA3B712C0A300E0C9FCA3 7E1270A212781238123C7E120E120F6C7E6C7EEA01F0EA00FCEB7F80011FB512C0130713 00222B7AA52F>50 D54 D<173017F0160116031607A2160FA2161F161B 163B1633167316E3A2ED01C316831503EE03F81507150EA2ED1C011538A2157015E0A2EC 01C0EC0380A2DA07007F140E92B5FC141F5C5C0270C7FC4A801301382003C038700780D8 780FC8127FEAFE3FD8FFFE160449169C49ED3FF86C4816E06C4816C06C48ED1F000007CB FC36337EAF38>65 D88 D<12E0B3B3B3AD034378B114>106 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fv cmmi8 8 40 /Fv 40 117 df11 DI<3907C0 07E0390FE03FF8391CF8783E393879E01E39307B801F38707F00126013FEEAE0FC12C05B 0081143F120149133EA20003147EA249137CA2000714FCA24913F8A2000F1301A2018013 F0A2001F1303A2010013E0120EC71207A215C0A2140FA21580A2141FA21500A2140E202C 7E9D23>17 D<147C49B4FC903803C78090380783C090381F03E0EB1E01133E017C13F013 F8A2EA01F0120313E01207A2EA0FC01403A2EA1F80A21407003F14E0130090B5FCA2397F 000FC0127EA2141F1580127C00FC14005CA2147EA248137C14FC00785B495AA2387C03E0 383C07C0495A001C90C7FCEA1E3EEA0FF8EA03E01C307DAE21>I<131C013EEB0380ED07 C0017E130F1680137CA201FC131F16005BA200015C153E5BA20003147E157C5BA20007EC FC08EDF8185BA2000F0101133816309038E003F002071370001F90380EF8609039F83C78 E090397FF03FC090391FC00F0048C9FCA2123EA2127EA2127CA212FCA25AA21270252C7E 9D2A>22 D<90B612F812035A4815F03A1E0380C000003C130000701301130700E05CEAC0 0638000E03A3131CA2133C140713381378A201F07FA21201A2D803E07FA20007130313C0 A26C486C5A251E7E9C29>25 D<0103B512F0131F137F90B612E03A01FC1F80003903F00F C03807C00748486C7E121F1300123EA25AA2140700FC5C5AA2140F5D141F92C7FC143E00 78133C147C007C5B383C01E0381F07C0D807FFC8FCEA01F8241E7D9C28>27 D31 D34 D39 D<123C127E12FFA4127E123C08087A 8714>58 D<123C127EB4FCA21380A2127F123D1201A312031300A25A1206120E5A5A5A12 6009157A8714>II<1670A216 F01501A24B7EA21507150DA2151915391531ED61FC156015C0EC0180A2EC03005C14064A 7F167E5C5CA25C14E05C4948137F91B6FC5B0106C7123FA25B131C1318491580161F5B5B 120112031207000FED3FC0D8FFF8903807FFFEA22F2F7DAE35>65 D<92387FC003913903FFF80791391FC03E0F91397E00071FD901F8EB03BF4948EB01FED9 0FC013004948147E49C8FC017E157C49153C485A120348481538485AA2485A1730484815 00A2127F90CAFCA35A5AA292381FFFFCA29238003FC0EE1F80163F1700A2127E5E167E7E A26C6C14FE000F4A5A6C7E6C6C1307D801F8EB1E3CD8007EEBFC3890391FFFE018010390 C8FC302F7CAD37>71 D<90273FFFFC0FB5FCA2D900FEC7EA3F80A24A1500A201015D177E 5CA2010315FE5F5CA2010714015F5CA2010F14035F5C91B6FC5B9139C00007E05CA2013F 140F5F91C7FCA249141F5F137EA201FE143F94C7FC5BA200015D167E5BA2000315FEB539 E03FFFF8A2382D7CAC3A>I<90383FFFFCA2903800FE00A25CA21301A25CA21303A25CA2 1307A25CA2130FA25CA2131FA25CA2133FA291C7FCA25BA2137EA213FEA25BA21201A25B A21203B512E0A21E2D7DAC1F>I77 DI<013FB6FC17E0903A00FE0007F0EE01FC4AEB007EA2010181A25C 1880010316005F5CA2010715FEA24A5C4C5A010F4A5A4C5A4AEB1F8004FFC7FC91B512F8 4914C00280C9FCA3133F91CAFCA35B137EA313FE5BA312015BA21203B512E0A2312D7DAC 2D>80 D<913807F00691383FFE0E9138F80F9E903903E001FE903807800049C7127C131E 49143CA2491438A313F81630A26D1400A27FEB7F8014F86DB47E15F06D13FC01077F0100 7F141F02011380EC003F151F150FA215071218A3150F00381500A2151EA2007C5C007E5C 007F5C397B8003E039F1F00F8026E07FFEC7FC38C00FF0272F7CAD2B>83 D<000FB8FCA23B1FC003F8003F0100151F001C4A130E123C003801071406123000704A13 0EA20060010F140C12E0485CA2141FC715005DA2143FA292C8FCA25CA2147EA214FEA25C A21301A25CA21303A25CA21307A25C130F131F001FB512F0A2302D7FAC29>I96 DI<13F8121FA21201A25BA21203A25BA21207A25BA2120FEBC7E0EB9FF8EBB83C381FF0 1EEBE01F13C09038800F80EA3F00A2123EA2007E131FA2127CA2143F00FC14005AA2147E A2147C14FC5C387801F01303495A383C0F806C48C7FCEA0FFCEA03F0192F7DAD1E>II<151FEC03FFA2EC003FA2153EA2157EA2157CA215FCA2 15F8A21401EB07E190381FF9F0EB7C1DEBF80FEA01F03903E007E0EA07C0120FEA1F8015 C0EA3F00140F5A007E1480A2141F12FE481400A2EC3F021506143E5AEC7E0E007CEBFE0C 14FC0101131C393E07BE18391F0E1E38390FFC0FF03903F003C0202F7DAD24>II<14FCEB03FF90380F839C90 381F01BC013E13FCEB7C005B1201485A15F8485A1401120F01C013F0A21403121F018013 E0A21407A215C0A2000F130F141F0007EB3F80EBC07F3803E1FF3800FF9F90383E1F0013 005CA2143EA2147E0038137C00FC13FC5C495A38F807E038F00F80D87FFEC7FCEA1FF81E 2C7E9D22>103 D<131FEA03FFA2EA003FA2133EA2137EA2137CA213FCA25BA21201143F 9038F1FFC09038F3C1F03803FF0001FC7F5BA2485A5BA25B000F13015D1380A2001F1303 5D1300140748ECC04016C0003E130F1580007E148191381F0180007C1403ED070000FCEB 0F06151E48EB07F80070EB01E0222F7DAD29>I<1307EB0F80EB1FC0A2EB0F80EB070090 C7FCA9EA01E0EA07F8EA0E3CEA1C3E123812301270EA607EEAE07C12C013FC485A120012 015B12035BA21207EBC04014C0120F13801381381F01801303EB0700EA0F06131EEA07F8 EA01F0122E7EAC18>I<15E0EC01F01403A3EC01C091C7FCA9147CEB03FE9038078F80EB 0E07131C013813C01330EB700F0160138013E013C0EB801F13001500A25CA2143EA2147E A2147CA214FCA25CA21301A25CA21303A25CA2130700385BEAFC0F5C49C7FCEAF83EEAF0 F8EA7FF0EA1F801C3B81AC1D>I<131FEA03FFA2EA003FA2133EA2137EA2137CA213FCA2 5BA2120115F89038F003FCEC0F0E0003EB1C1EEC387EEBE07014E03807E1C09038E38038 49C7FC13CEEA0FDC13F8A2EBFF80381F9FE0EB83F0EB01F81300481404150C123EA2007E 141C1518007CEBF038ECF83000FC1470EC78E048EB3FC00070EB0F801F2F7DAD25>I<13 7CEA0FFCA21200A213F8A21201A213F0A21203A213E0A21207A213C0A2120FA21380A212 1FA21300A25AA2123EA2127EA2127CA2EAFC08131812F8A21338133012F01370EAF860EA 78E0EA3FC0EA0F000E2F7DAD15>I<27078007F0137E3C1FE01FFC03FF803C18F0781F07 83E03B3878E00F1E01263079C001B87F26707F8013B00060010013F001FE14E000E015C0 485A4914800081021F130300015F491400A200034A13076049133E170F0007027EEC8080 188149017C131F1801000F02FCEB3F03053E130049495C180E001F0101EC1E0C183C0100 49EB0FF0000E6D48EB03E0391F7E9D3E>I<3907C007E0391FE03FF83918F8783E393879 E01E39307B801F38707F00126013FEEAE0FC12C05B00815C0001143E5BA20003147E157C 5B15FC0007ECF8081618EBC00115F0000F1538913803E0300180147016E0001F010113C0 15E390C7EAFF00000E143E251F7E9D2B>I<903807E03090381FF87090387C1CF0EBF80D 3801F00F3903E007E0EA07C0000F1303381F800715C0EA3F00A248130F007E1480A300FE 131F481400A35C143E5A147E007C13FE5C1301EA3E07EA1F0E380FFCF8EA03F0C7FC1301 5CA313035CA21307A2EBFFFEA21C2B7D9D20>113 D<3807C01F390FF07FC0391CF8E0E0 383879C138307B8738707F07EA607E13FC00E0EB03804848C7FCA2128112015BA21203A2 5BA21207A25BA2120FA25BA2121FA290C8FC120E1B1F7E9D20>II<130E131FA25BA2133EA2137EA2137CA213FCA2B512F8 A23801F800A25BA21203A25BA21207A25BA2120FA25BA2001F1310143013001470146014 E0381E01C0EB0380381F0700EA0F0EEA07FCEA01F0152B7EA919>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fw cmmi12 12 71 /Fw 71 123 df11 DI<1578913807 FFE0021F13FC91383C7FFEEC7007EC6003ECE0004A13381600A280A380A280147CA2147E 143E143F816E7EA26E7E81140781EC3FFC14FF903803E1FEEB07C190381F00FF133E49EB 7F805B0001143F485A484814C049131F120F485AA248C7FC150F5A127EA300FEEC1F805A A316005A5DA2153E157E157CA26C5C127C4A5A6C495AA26C495A6C6C485A6C6C48C7FC38 03E07C3800FFF0EB1FC027487CC62B>14 DI<01F8EB03FCD803FEEB1FFFD8071F90387C0FC03B0E 0F80E007E0001C9038C3C003271807C70013F002CE1301003801DC14F8003013D8EB0FF8 00705B00605BA200E0491303D8C01F15F05C12001607133F91C713E0A2160F5B017E15C0 A2161F13FE491580A2163F1201491500A25E120349147EA216FE1207495CA21501120F49 5CEA0380C81203A25EA21507A25EA2150FA25EA2151FA25EA2153FA293C7FC150E2D417D AB30>17 D<157E913801FF80913807C3E091381F01F0EC3E004A13F814FC4948137C495A 5C0107147E495A131F5C133F49C7127FA213FEA212015B12034914FF1207A25B000F15FE 1501A2485AA21503003F15FC5B90B6FCA24815F89038800007A2150F00FF15F090C7FCA2 ED1FE0A25AED3FC0A21680157F16005A15FEA24A5AA25D14035D4A5A007C495AA24A5A00 7E49C7FC003E133E5C001E5B6C485A380783C06CB4C8FCEA00FC28477CC52D>I21 D<147002F8140E0101153FA301035DA24A147EA2010715FEA24A5CA2010F1401A24A5CA2 011F1403A24A5CA2013F1407A291C75BA249140FA2017E5DA201FE021F1318183849ED80 30A20001033F13701860EE7F005E486C16E0DB01DF13C09238039F016DD9071F13804890 39801E0F83903BF7C078078700903AE1FFE003FE903AE07F8000F8000F90CAFCA25BA212 1FA25BA2123FA290CBFCA25AA2127EA212FEA25A123835417DAB3B>I<010FB712E0013F 16F05B48B812E04817C02807E0060030C7FCEB800EEA0F00001E010C13705A0038011C13 605A0060011813E000E013381240C7FC5C4B5AA214F014E01301150314C01303A3EB0780 82130FA2EB1F00A34980133E137EA24980A2000114015BA26C48EB00E0342C7EAA37>25 DI<0203B612E0021F15 F091B7FC4916E0010716C090270FF80FF8C7FC90381FC00349486C7E017EC7FC49147E48 5A4848143E0007153F5B485AA2485AA2123F90C8FC5E48157E127EA216FE00FE5D5A1501 5EA24B5A007C5D15074B5A5E6C4AC8FC153E6C5C5D390F8003F03907C007C02601F03FC9 FC38007FFCEB1FE0342C7DAA37>I<161CA21618A21638A21630A21670A21660A216E0A2 5EA21501A25EA21503A293C8FCA25DED7FE0913807FFFE91391FC63F809139FE0E07C0D9 01F8EB03F0903A07E00C00F8D91FC08090263F001C137E017E814913184848ED1F800003 1438485A4848013014C0A248481370A248481360A248C712E0A24B133F481780481301A2 4B137F180014034816FE92C7FC4C5A6C49495AA2007E0106495A4C5A6C010E495A4C5A26 1F800C49C7FC000F15FC3A07C01C01F8D803E0EB07E03A01F8181F80D8007E01FEC8FC90 381FFFF801011380D90030C9FCA21470A21460A214E0A25CA21301A25CA21303A291CAFC A332597BC43A>30 D<137E48B46C150626078FE0150E260607F0151C260E03F81538000C 6D1570D81C0116E000006D15C0010015016EEC03806EEC0700170E6E6C5B5F5F6E6C1360 17E04C5A6E6C485A4CC7FC0207130E6F5A5E1630913803F8705EEDF9C06EB45A93C8FC5D 6E5A81A2157E15FF5C5C9138073F80140E141C9138181FC014381470ECE00FD901C07FEB 038049486C7E130E130C011C6D7E5B5B496D7E485A48488048C8FC000681000E6F137048 EE806048033F13E04892381FC0C048ED0FE348923803FF00CA12FC37407DAB3D>I<1730 A317701760A317E05FA316015FA3160394C8FCA35E1606A3160E160C013E1607D9FF80ED 1F802603C3C0011CEB3FC0260703E01318260601F0157F000E173F001C1538D818030230 131F0038170F0030170700701570D86007026013035CA2D8E00F02E0148000C049491301 EA001F4A150303011500013F5C1400604901031406017E91C7FC180E180C01FE49141C49 01061418183860030E1460030C14E04D5A4D5A031C49C7FC0318130E017E5D5F6D01385B 90261F80305BD90FC0EB03C0D907F0010FC8FC903901FE707C9039003FFFF002031380DA 0060C9FC15E05DA314015DA3140392CAFCA35C1406A3140E140C3A597DC43F>I<011016 0E0138163F0178EE7F80137001F016FF4848167F5B0003173F49161F120790CA120FA200 0E1707A248180015060018140FA20038021E14061230A2180E00704A140C1260181CA203 381418183800E05C6015F86C01015D170114030078D907BC495ADA0FBE1307007CD91F3E 495A007ED97E3F013FC7FC3B7F83FE1FE0FF263FFFFCEBFFFE4A6C5B6C01F05C6CD9C007 5B6CD9000113C0D801FC6D6CC8FC392D7FAB3D>II<177F0130913803FFC00170020F13E0494A13F048484A13F8 4848EC7F0190C838F8007C484A48133C00064A48131C000E4B131E000C4A48130E001C92 C7FC0018140E150C0038021C1406003014185D180E00704A140C1260154003C0141C00E0 17184A5A4817386C17304AC8127018E01260007049EC01C0EF03800078010614070038EE 0F00003C010E141E6C167CD81F805D6C6C48EB03F0D807F0EC0FE0D803FEEC3FC02801FF FC03FFC7FC6C6CB55A6D14F8010F14E0010114809026007FF8C8FC02F8C9FCA25CA21301 A3495AA31307A25C130FA4131F5C6DCAFC37417BAB40>39 D<133EEA01FF5AEA0FFEEA1F E0EA3F00127E127C5AA25AA47EA2127C127E7EEA1FE0EA0FFEEA03FF7EEA003E10187BAE 1B>44 D<121EEA7F80A2EAFFC0A4EA7F80A2EA1E000A0A78891B>58 D<121EEA7F8012FF13C0A213E0A3127FEA1E601200A413E013C0A312011380120313005A 1206120E5A5A5A12600B1D78891B>II<1618163C16 7CA2167816F8A216F01501A216E01503A216C01507A21680150FA2ED1F00A2151E153EA2 153C157CA2157815F8A25D1401A24A5AA25D1407A25D140FA292C7FC5CA2141E143EA214 3C147CA25CA25C1301A25C1303A25C1307A25C130FA291C8FC5BA2133EA2133C137CA213 7813F8A25B1201A25B1203A2485AA25B120FA290C9FC5AA2121E123EA2123C127CA21278 12F8A25A126026647BCA31>I<127012FCB4FCEA7FC0EA1FF0EA07FCEA01FF38007FC0EB 1FF0EB07FE903801FF809038007FE0EC1FF8EC03FE913800FF80ED3FE0ED0FF8ED03FF03 0013C0EE3FF0EE0FFCEE01FF9338007FC0EF1FF0EF07FCEF01FF9438007FC0F01FE0A2F0 7FC0943801FF00EF07FCEF1FF0EF7FC04C48C7FCEE0FFCEE3FF0EEFFC0030390C8FCED0F F8ED3FE0EDFF80DA03FEC9FCEC1FF8EC7FE0903801FF80D907FECAFCEB1FF0EB7FC04848 CBFCEA07FCEA1FF0EA7FC048CCFC12FC12703B3878B44C>I<1830187018F0A217011703 A24D7EA2170F171FA21737A2176717E717C793380187FCA2EE0307EE07031606160CA216 181638163004607FA216C0030113011680ED0300A21506150E150C5D845D03707F15605D A24A5A4AB7FCA25C0206C87F5C021C157F14185CA25C14E05C495A8549C9FC49163F1306 130E5B133C137C01FE4C7ED807FFED01FF007F01F0027FEBFFC0B5FC5C42477DC649>65 D<91B87E19F019FC02009039C00003FF6F480100138003FFED3FC01AE093C8121FF10FF0 A24A17F84B1507A314035D190FA2020717F04B151F1AE0193F020F17C04BED7F80F1FF00 4E5A021F4B5A4B4A5AF01FF0F03FC0023F4AB4C7FC4BEB1FFC92B612F018FEDA7FC0C7EA 7F804BEC1FC0F00FF0727E02FF6F7E92C8FC727EA249835CA313035CA301075F4A1503A2 4E5A130F4A4B5A4E5AA2011F4C5A4A4B5A4D485A013F4B48C7FCEF0FFC4AEC3FF801FF91 3801FFE0B9128005FCC8FC17C045447CC34A>I<4CB46C1318043F01F013384BB512FC03 07D9007E1378DB1FF090380F80F0DB7F80EB03C1DA01FEC7EA01C34A48EC00E7DA0FF0ED 7FE04A48153F4A5A02FFC9121F494817C04948160F495A130F4A178049481607495A137F 4948170091CAFC5A485A1906485AA2485A96C7FC121F5BA2123F5BA3127F5BA4485AA419 C0A2180161127F180396C7FC6018066C6C160E601818001F17386D5E000F5F6D4B5A6C6C 4B5A00034CC8FC6C6C150E6C6C153C017F5DD93FC0EB01E0D91FF0EB0FC0D907FE017FC9 FC0101B512FCD9003F13E0020790CAFC45487CC546>I<91B87E19F019FC02009039C000 07FF6F489038007FC003FFED1FE0737E93C86C7E737E19014A707E5D1A7FA20203EF3F80 5DA21BC014075DA3140F4B17E0A3141F4B17C0A3143F4B167FA3027F18804B16FFA302FF 180092C95A62A24917034A5F19076201034D5A5C4F5A620107173F4A5F4FC7FC19FE010F 4C5A4A15034E5AF00FE0011F4C5A4A4B5A06FFC8FC013FED01FCEF0FF84AEC3FE001FF91 3803FF80B848C9FC17F094CAFC4B447CC351>I<91B912FCA3020001C0C7123F6F48EC03 F803FF1501190093C91278A21A385C5DA3020317305DA314074B1460A218E0020F4B1300 5DA21701021F5D4B13031707170F023F027FC8FC92B6FCA391397FC0007E4B131EA2170E 02FF140C92C7FCA2171C49031813035C611906010392C7FC4A160E190C191C010717184A 163819301970130F4A5E180161011F16034A15074E5A013F163F4EC7FC4AEC03FF01FFED 3FFEB9FCA26046447CC348>I<91B912F8A3020001C0C7123F6F48EC07F003FF15031901 93C9FCA21A705C5DA3020317605DA314075D18C01701020F4B13005DA21703021F92C8FC 4B5BA25F023F141E4B13FE92B5FCA24A5CED8000173CA202FF141892C7FCA21738491530 5CA21770010315604A91C9FCA313075CA3130F5CA3131F5CA2133FA313FFB612F8A34544 7CC33F>I<4CB46C1318043F01F013384BB512FC0307D9007E1378DB1FF090380F80F0DB 7F80EB03C1DA01FEC7EA01C34A48EC00E7DA0FF0ED7FE04A48153F4A5A02FFC9121F4948 17C04948160F495A130F4A178049481607495A137F4948170091CAFC5A485A1906485AA2 485A96C7FC121F5BA2123F5BA3127F5BA4485A4CB612805EA293C7EBE000725AA3007F60 A218FF96C7FCA26C7E5F606C7EA2000F16036D5E6C6C15070003160F6C6C151F6C6CED3D F8D97F8014786D6CEB01E0D91FF0903807C078D907FE90387F00700101B500FC1330D900 3F01F090C8FC020790CAFC45487CC54D>I<91B6D8E003B61280A3020001E0C70003EB80 00DB7F806E48C7FC03FF1503A293C85BA219075C4B5EA2190F14034B5EA2191F14074B5E A2193F140F4B5EA2197F141F4B5EA219FF143F92B8C8FCA3DA7FC0C712014B5DA2180314 FF92C85BA218075B4A5EA2180F13034A5EA2181F13074A5EA2183F130F4A5EA2187F131F 4A5EA2013F16FFA24A93C9FCD9FFE002037FB6D8E003B67EA351447CC351>I<027FB512 F8A217F09139007FF000ED3FC0157FA25EA315FF93C7FCA35C5DA314035DA314075DA314 0F5DA3141F5DA3143F5DA3147F5DA314FF92C8FCA35B5CA313035CA313075CA3130F5CA2 131FA25CEB7FF0007FB512F0B6FCA22D447DC32B>I<031FB512FC5D18F89239000FFE00 705AA35FA2160FA25FA2161FA25FA2163FA25FA2167FA25FA216FFA294C7FCA25DA25EA2 1503A25EA21507A25EA2150FA25EA2151FA25EA2153FA25EEA0F80D83FE0137F5E127FA2 4BC8FC485A4A5A1300006C495A0060495A0070495A0030495A0038EB3F806C49C9FC380F 81FC3803FFF038007F80364679C336>I<91B600E049B512C0A3020001E0C8383FF800DB 7F80ED1FE003FF94C7FC1A3E93C9127862F101C04A4C5A4B4BC8FC191C6102035E4B5DF0 03804EC9FC0207150E4B14386060020F4A5A4B0107CAFC170E5F021F14784B13F84C7E16 03023F130F4B487E163BEEE1FF91387FC1C1DB83807FED8700159CDAFFB86D7E5D03C06D 7E5D4990C7FC4A6E7EA2717E13034A811707A201076F7E5C717EA2130F4A6E7FA2727E13 1F5C727E133F854A82D9FFE04B7EB600E0010FB512E05FA252447CC353>I<91B612F8A3 020001E0C8FC6F5A4B5AA293C9FCA35C5DA314035DA314075DA3140F5DA3141F5DA3143F 5DA3147F5DA314FF92CAFCA35B4A16C0A21801010317804A15031900A201075E4A150618 0E181E010F161C4A153C18381878011F16F84A4A5A1703013F150F4D5A4A14FF01FF0207 5BB9FCA2603A447CC342>I<91B500C0933803FFFE63630200F1FE00DB6FE0EE1BF803EF 171F1B3703CFEF67F0A21BCF0201EF018F038F60DB87F0ED030F1B1F020317060307040C 5BA2F2183F020717300206616F6C15601B7F020E17C0020CDC018090C7FCA24F485A021C 16060218606F6C5C1A0102381618023004305BA2F16003027016C00260606F6CEB01801A 0702E0ED03004A03065CA24E130F01015E4A60047F5B1A1F01035E91C74A5CA24D48133F 494BC7FC010661EE3F861A7F010E158C010C039892C8FCA205B05C011C15E00118600138 6E5A190101785D01FC92C75BD803FFEF07FEB500F8011E0107B512FE161C160C5F447BC3 5E>I<91B500C0020FB5128082A2DA007F9239007FE00070ED1F8074C7FCDBEFF8150E15 CF03C7160C70151C1401DB83FE1518A2DB81FF1538140303001630831A704A6D7E020617 60163F7114E0140E020C6D6C5CA2706C1301141C021801075D83190302386D7E023094C8 FC1601715B147002606DEB8006A294387FC00E14E04A023F130C18E0191C0101ED1FF04A 1618170FF0F838130391C83807FC30A2943803FE705B01060301136018FF19E0010E8101 0C5F187FA2131C0118705A1338181F137801FC70C9FCEA03FFB512F884180651447CC34E >I<91B712FEF0FFE019F802009039C0000FFE6F48EB01FF03FF9138007F80F13FC093C8 EA1FE0A24AEE0FF0A25D1AF81403A25DA21407F11FF05DA2020FEE3FE0A24B16C0197F02 1F1780F1FF004B4A5A4E5A023F4B5A4E5A4BEC3FC006FFC7FC027FEC07FC92B612F01880 0380CAFC14FFA292CBFCA25BA25CA21303A25CA21307A25CA2130FA25CA2131FA25CA213 3FA25CEBFFE0B612E0A345447CC33F>80 D<91B712F018FF19E002009039C0003FF86F48 EB07FC03FFEC01FEF0007F93C8EA3F801AC0F11FE05C5D1AF0A214035DA30207EE3FE05D A2F17FC0020F17804B15FF1A004E5A021F4B5A4B4A5AF00FE04E5A023F037FC7FC4BEB03 FCEF1FF092B612804A4AC8FC923980007F80EF0FC0EF07F002FF6E7E92C77F1701845B4A 1400A2170113035CA2170313075CA24D5A130F5CA3011F18185CA2013F4C13381A304A6F 1370D9FFE0020314E0B600E0ED01C00501EB0380943900FE0F00CBEA3FFEF007F045467C C34A>82 D<9339FF8001800307EBF003033F13FC9239FF007E07DA01F8EB0F0FDA07E090 38079F004A486DB4FC4AC77E023E804A5D187E5C495A183C495AA213074A1538A3130F18 3080A295C7FC806D7E8014FF6D13E015FC6DEBFFC06D14FC6E13FF6E14C0020F80020314 F8EC003F03077F9238007FFE160F1603707E8283A283A21206A4000E163EA2120C177E00 1E167CA25F5F003F15014C5A6D4A5A4C5A486C4AC8FC6D143ED87CF85CD8787E495A3AF0 1FC00FE0D8E007B51280010149C9FC39C0003FF039487BC53C>I<48BA12C05AA291C7D9 80001380D807F092C7121F4949150F0180170748C75B1903120E48020316005E12181238 003014074C5C00701806126000E0140F485DA3C8001F92C7FC5EA3153F5EA3157F5EA315 FF93CAFCA35C5DA314035DA314075DA3140F5DA3141F5DA3143F5DA2147FA214FF01037F 001FB612FCA25E42447EC339>I<003FB500F80103B512E0A326003FF8C8381FF800D91F E0ED07E0013F705A615C96C7FC60017F16065CA2180E01FF160C91C9FCA2181C4817185B A21838000317305BA21870000717605BA218E0120F495EA21701121F495EA21703123F49 93C8FCA25F127F491506A2170E00FF160C90C9FC171CA21718173817304816705F6C5E6C 15014C5A4CC9FC6C150E6D141E001F5D6D5C6C6CEB01E06C6C495A6C6CEB1F80C6B401FE CAFC90387FFFF8011F13E0010190CBFC43467AC342>I<007FB56C91381FFFF8B65DA200 0101E0C8000313006C0180ED01FCF000F0614E5AA2017F4C5A96C7FC1806A2606E5DA201 3F5E1870186060A24D5A6E4AC8FCA2011F1506170E170C5FA26E5C5FA2010F5D16015F4C C9FCA26E13065EA201075C5EA25E16E06E5B4B5A13034BCAFC1506A25D151CECFE185D13 015D5DA26E5AA292CBFC5C13005C5CA25CA25C45467BC339>II<023FB500E0011F B5FCA39126007FFEC7000313E0DB3FF8913801FE006F486E5A1AF06F6C4A5A626F6C4A5A 0706C7FC190E6F6C5C616F6C5C6171485A6F5D4EC8FC93387FC00660706C5A6060706C5A 17F193380FFB8005FFC9FC5F705AA2707EA3707E5E04067F5E93381C7FC0163816704C6C 7EED01C04B486C7E160015064B6D7E5D4B6D7E5D5D4A486D7E14034AC76C7E140E5C4A6E 7F143002E06F7E495A0103707E495A131F496C4B7E2603FFE04A487E007F01FC021FEBFF F0B5FCA250447EC351>II<020FB812C05C1A80932680000113 0003F8C7FCDA3FE04A5A03804A5A92C8485A027E4B5A027C4B5A02784B5A4A4B5AA24A4A 90C7FC4A4A5A01014B5A4D5A4A4A5A01034B5A91C8485A4D5AA290C84890C8FC4C5A4C5A 4C5A4C5A4C5A4C5A4C5AA24B90C9FC4B5A4B5A4B5A4B5A4B5A4B5AA24B5A4A90CAFC4A5A 4A4814064A5A4A5A4A48140E4A48140CA24A48141C4990C8121849481538495A49485D49 5A494815F049485D1701494814034890C8485A4848150F4848151F48484B5A484815FF48 481403043F90C8FC48B8FCB9FC5F42447BC343>I96 DIII< EE01FC16FFA3EE03F816011603A217F0A21607A217E0A2160FA217C0A2161FA21780A216 3FA21700EC0FC091387FF07F903801F838903907E01C7E90380FC00E90393F0007FE4913 0301FE5C485A491301120348485C120F491303121F5E485A1507127F495CA2150F12FF90 C75BA2151FA2485DA2033F13301770EE0060A24B13E017C015FE007E130102031301003E D9073E1380003F010E13036C011C14006C6C486C5A3A07C0F00F0E3A01FFC007FC3A007F 0001F02E467CC433>II<157E913803FF8091390FC1E0E091391F0073F0027E 13334A133F4948131F010315E04948130F495AA2494814C0133F4A131F137F91C713805B 163F5A491500A25E120349147EA216FEA2495CA21501A25EA21503150700015D150F0000 141F6D133F017CEB77E090383E01E790381F078F903807FE0FD901F85B90C7FC151FA25E A2153FA293C7FCA2001C147E007F14FE485C4A5A140348495AEC0FC000F8495A007C01FE C8FC381FFFF8000313C02C407EAB2F>103 D<14FE137FA3EB01FC13001301A25CA21303 A25CA21307A25CA2130FA25CA2131FA25CED3FC090393F81FFF0913887C0FC91380E007E 023C133ED97F70133F4A7F4A14805C13FF91C7FC5BA24848143F17005BA200035D167E5B A2000715FE5E5B1501000F5DA24913035E001F1607030713064914E0150F003FEDC00E17 0C90C7141CEE80184816381730007E167017E000FE91380781C0EEC38048913801FF0000 38EC007C30467BC438>I<141E143F5C5CA3147E143891C7FCAE133EEBFF803801C3C038 0781E0380601F0120E121CEA180312381230A2EA700700605BA2EAE00F00C05BEA001F5C A2133F91C7FCA25B137E13FE5BA212015BEC03800003140013F01207495A1406140E140C EBC01C141814385C00035BEBE1C0C6B45A013EC7FC19437DC121>I<163C16FEA21501A3 16FCED00701600AE15FCEC03FF91380F0780021C13C091383803E0147014E014C01301EC 8007130314005B0106130F130E010C14C090C7FC151FA21680A2153FA21600A25DA2157E A215FEA25DA21401A25DA21403A25DA21407A25DA2140FA25DA2141F5DA2143F001C91C7 FC127F48137E5CA248485AEB03E038F807C038781F80D83FFEC8FCEA07F0275681C128> I<14FE137FA3EB01FC13001301A25CA21303A25CA21307A25CA2130FA25CA2131FA25C16 3F013FECFFC0923803C0E09138000703ED1E0F491338ED701F017E13E0EC01C001FE0180 13C00203EB07004948C8FC140E00015B5C495A5C3803FBC001FFC9FC8014F83807F1FE90 38F03F809038E00FE06E7E000F130381EBC001A2001FED01C017801380A2003F15031700 010013F05E481506160E007E150C161C00FE01005BED787048EC3FE00038EC0F802B467B C433>II<01F8D903FCEC7F80D803FED91FFF 903803FFE0D8071F903B7C0FC00F81F83E0E0F80E007E01C00FC001C9026C3C003017813 7C271807C700D9F0E0137E02CE902601F1C0133E003801DCDAFB80133F003001D892C7FC D90FF814FF0070495C0060495CA200E04949485CD8C01F187E4A5C1200040715FE013F60 91C75BA2040F14014960017E5D1903041F5D13FE494B130762043F160E0001060F130C49 92C713C0191F4CED801C00031A1849027E1638F2003004FE167000071A60494A16E0F201 C0030192380F0380000FF18700494AEC03FED80380D90070EC00F84F2D7DAB55>I<01F8 EB03FCD803FEEB1FFFD8071F90387C0FC03B0E0F80E007E03A0C07C3C003001CD9C7007F 001801CE1301003801DC80003013D8EB0FF800705B00605BA200E0491303D8C01F5D5C12 001607013F5D91C7FCA2160F495D137E161F5F13FE49143F94C7FC187000014B13604914 7E16FE4C13E0000317C049150104F81380170300071700495D170EEE781C000FED7C3849 EC1FF0D80380EC07C0342D7DAB3A>I<91380FC00391383FF0079138F83C0F903903E00E 1E90390FC0063E90381F800790393F00037E4914FC01FE1301485AA2484814F812075B00 0F140316F0485AA2003F14074914E0A3007F140F4914C0A3151F90C713805AA2153F6C15 00A2127E5D007F14FE6C1301A214036C6C485A000F131E3807C0383803E0F13901FFC1F8 38003F01130014035DA314075DA3140F5DA2141FA2143F011FB51280A21600283F7DAB2B >113 D<01F8EB0FC0D803FEEB7FF0D8070FEBF038000E903883C07C3A0C07C701FC001C 13CE0018EBDC03003813D8003013F8D90FF013F800709038E000E0006015005C12E0EAC0 1F5C1200A2133F91C8FCA35B137EA313FE5BA312015BA312035BA312075BA3120F5BEA03 80262D7DAB2C>II<141C147EA3 14FE5CA313015CA313035CA313075CA2007FB512FCB6FC15F839000FC000A2131F5CA313 3F91C7FCA35B137EA313FE5BA312015BA312035BA21570000714605B15E015C0000F1301 01C013801403EC070000071306140E5C6C6C5A000113F03800FFC0013FC7FC1E3F7EBD23 >I<133ED9FF8014E02603C3C0EB03F0380703E0380601F0000E1507121CD818035D1238 0030150FA2D870075D00605B161FEAE00F00C0495CEA001F4A133FA2013F92C7FC91C7FC 5E5B017E147EA216FE13FE495CA20301EB01801703484802F81300A25F0303130616F000 001407030F130E6D010D130C017C011D131C033913186D9038F0F838903A1F03C0787090 3A07FF803FE0903A01FC000F80312D7DAB38>I<013E140ED9FF80EB3F802603C3C0137F 380703E0380601F0120E121CD81803143F0038151F0030150FA2D87007140700605BA2D8 E00F150000C0497FEA001F4A5B1606133F91C7FC160E49140C137EA2161C01FE14185B16 38163016704848146016E05E150100005D15036D49C7FC1506017C130E017E5B6D137890 380F81E06DB45AD900FEC8FC292D7DAB2F>I<013E1738D9FF80D901C013FC2603C3C090 3907E001FE380703E0380601F0000E150F001C16C0D8180316000038187E0030031F143E 00705ED86007171E5C163FD8E00F92C7121C00C049160CEA001F4A49141C047E1418133F 91C7FC04FE1438491730017E5CA20301157001FE1760495C19E019C0A249494813011980 18031900606D0107140670130E017C010F5C017E010C1418013ED91CFC13386DD9387E13 F0903B0FC0F01F01C0903B03FFC00FFF809028007F0001FEC7FC3F2D7DAB46>I<02FCEB 07E0903A03FF801FFC903A0F07C0781E903A1C03E0E01F903A3801F1C07FD97000138049 01FB13FF4848EBFF00495B000316FE90C71438484A130012061401000E5C120CC7FC1403 5DA314075DA3140F5DA3021F143817305D1770023F1460121E003F16E0267F807FEB01C0 026F148000FF01EF1303D901CFEB070000FE903887C00E267C03835B3A3C0F01E0783A1F FC00FFE0D803F0EB3F80302D7EAB37>I<133ED9FF8014E02603C3C0EB03F0380703E038 0601F0000E1507001C16E0EA180312380030150F007016C0EA60075C161FD8E00F158000 C05BEA001F4A133F1700133F91C7FC5E49147E137EA216FE01FE5C5BA215015E485AA215 035EA200001407150F6D5C017C131F153F6D13FF90391F03CFC0903807FF8F903801FC0F 90C7121F5EA2153F93C7FCD807C05BD81FE0137E5DA24848485A4A5A01805B39380007C0 0018495A001C49C8FC6C137C380781F83803FFE0C66CC9FC2C407DAB30>I<027CEB0180 49B413034901801300010F6D5A49EBE00E6F5A90393F03F838903978007EF80170EB1FF0 0160EB01E001E05C49495A90C748C7FC150E5D5D5D5D4A5A4A5A4AC8FC140E5C5C5C5CEB 03C049C9FC130E49141C4914185B49143848481430491470D8039014F048B4495A3A0FEF C007C0391E03F01FD81C01B55A486C91C7FC485C00606D5A00E0EB3FF048EB0FC0292D7C AB2D>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fx cmsy10 12 35 /Fx 35 107 df<007FB912E0BA12F0A26C18E03C04789A4D>0 D<121FEA3F80EA7FC0EA FFE0A5EA7FC0EA3F80EA1F000B0B789E1C>I<0060160600F8160F6C161F007E163F6C16 7E6C6C15FC6C6CEC01F86C6CEC03F06C6CEC07E06C6CEC0FC06C6CEC1F80017EEC3F006D 147E6D6C5B6D6C485A6D6C485A6D6C485A6D6C485A6D6C485ADA7E3FC7FCEC3F7E6E5A6E 5A6E5AA24A7E4A7EEC3F7EEC7E3F4A6C7E49486C7E49486C7E49486C7E49486C7E49486C 7E49C7127E017E8049EC1F804848EC0FC04848EC07E04848EC03F04848EC01F84848EC00 FC48C9127E007E163F48161F48160F00601606303072B04D>I8 D10 D<49B4FC010F13E0013F13F8497F3901FF01FF3A03F8003F80D807E0EB0FC0 4848EB07E04848EB03F090C71201003EEC00F8A248157CA20078153C00F8153EA248151E A56C153EA20078153C007C157CA26C15F8A26CEC01F06D13036C6CEB07E06C6CEB0FC0D8 03F8EB3F803A01FF01FF0039007FFFFC6D5B010F13E0010190C7FC27277BAB32>14 D<49B4FC010F13E0013F13F8497F48B6FC4815804815C04815E04815F0A24815F8A24815 FCA3B712FEA96C15FCA36C15F8A26C15F0A26C15E06C15C06C15806C15006C6C13FC6D5B 010F13E0010190C7FC27277BAB32>I<037FB612E00207B712F0143F91B812E0010301C0 C9FCD907FCCAFCEB0FE0EB3F8049CBFC13FC485A485A485A5B485A121F90CCFC123EA212 3C127CA2127812F8A25AA87EA21278127CA2123C123EA27E7F120F6C7E7F6C7E6C7E6C7E 137E6D7EEB1FE0EB07FC6DB47E010090B712E0023F16F01407020016E092CAFCB0001FB9 12E04818F0A26C18E03C4E78BE4D>18 D<19E0F003F0180FF03FE0F0FF80943803FE00EF 0FF8EF3FE0EFFF80DC03FEC7FCEE0FF8EE3FE0EEFF80DB03FEC8FCED1FF8ED7FE0913801 FF80DA07FEC9FCEC1FF0EC7FC04948CAFCEB07FCEB1FF0EB7FC04848CBFCEA07FCEA1FF0 EA7FC048CCFCA2EA7FC0EA1FF0EA07FCEA01FF38007FC0EB1FF0EB07FCEB01FF9038007F C0EC1FF0EC07FC913801FF809138007FE0ED1FF8ED07FE923800FF80EE3FE0EE0FF8EE03 FE933800FF80EF3FE0EF0FF8EF03FE943800FF80F03FE0F00FF01803F000E01900B0007F B912E0BA12F0A26C18E03C4E78BE4D>20 D<127012FCB4FCEA7FC0EA1FF0EA07FCEA01FF 38007FC0EB1FF0EB07FCEB01FF9038007FC0EC1FF0EC07FC913801FF809138007FE0ED1F F8ED07FE923800FF80EE3FE0EE0FF8EE03FE933800FF80EF3FE0EF0FF8EF03FE943800FF 80F03FE0F00FF0A2F03FE0F0FF80943803FE00EF0FF8EF3FE0EFFF80DC03FEC7FCEE0FF8 EE3FE0EEFF80DB03FEC8FCED1FF8ED7FE0913801FF80DA07FEC9FCEC1FF0EC7FC04948CA FCEB07FCEB1FF0EB7FC04848CBFCEA07FCEA1FF0EA7FC048CCFC12FC1270CDFCB0007FB9 12E0BA12F0A26C18E03C4E78BE4D>I24 D<037FB612E00207B712F0143F91B812E0010301C0C9FCD907FCCAFCEB0FE0EB3F8049CB FC13FC485A485A485A5B485A121F90CCFC123EA2123C127CA2127812F8A25AA87EA21278 127CA2123C123EA27E7F120F6C7E7F6C7E6C7E6C7E137E6D7EEB1FE0EB07FC6DB47E0100 90B712E0023F16F01407020016E03C3A78B54D>26 D<1AF0A3861A78A21A7C1A3CA21A3E 1A1E1A1F747EA2747E747E87747E747E1B7E87757EF30FE0F303F8007FBC12FEBE1280A2 6CF3FE00CEEA03F8F30FE0F31F8051C7FC1B7E63505A505A63505A505AA250C8FC1A1E1A 3E1A3CA21A7C1A78A21AF862A359347BB264>33 D39 D<18034E7E85180385180185727E1978197C8585737E86737E737E007FBA7EBB7E86 6C85CDEA0FC0747EF203F8F200FEF37F80F31FE0F307FC983801FF80A2983807FC00F31F E0F37F8009FEC7FCF203F8F207E0505A007FBBC8FCBB5A626C61CCEA03F04F5A4F5A624F C9FC193E61197819F84E5A6118036118076172CAFC59387BB464>41 D<92B6FC02071580143F91B7120001030180C8FCD907FCC9FCEB1FE0EB3F80017ECAFC5B 485A485A485A5B485A121F90CBFC123EA2123C127CA2127812F8A25AA2B9FC1880A21800 00F0CBFCA27EA21278127CA2123C123EA27E7F120F6C7E7F6C7E6C7E6C7E137E6D7EEB1F E0EB07FC6DB47E010090B6FC023F1580140702001500313A78B542>50 D<1706170F171FA2173EA2177CA217F8A2EE01F0A2EE03E0A2EE07C0A2EE0F80A2EE1F00 A2163EA25EA25EA24B5AA24B5AA24B5AA24B5AA24BC7FCA2153EA25DA25DA24A5AA24A5A A24A5AA24A5AA24AC8FCA2143EA25CA25CA2495AA2495AA2495AA2495AA249C9FCA2133E A25BA25BA2485AA2485AA2485AA2485AA248CAFCA2123EA25AA25AA25A1260305C72C600 >54 D<126012F0B012FC12FEA212FC12F0B0126007267BAB00>I<0060171800F0173C6C 177CA200781778007C17F8A2003C17F0003E1601A26CEE03E0A26C17C06D1507A2000717 806D150FA26C6CED1F00A20001161E6D153EA20000163C90B712FCA26D5DA2013CC85A01 3E1401A2011E5D011F1403A26D5D6E1307A26D6C495AA2010392C7FC6E5BA20101141E6E 133EA26D6C5BA202781378027C13F8A2023C5BEC3E01A26E485AA2020F5B1587A202075B 15CFA26EB4C8FCA26E5AA36E5AA315781530364780C437>I<007FB712E0B812F0A27ECA FCB3AA001FB7FC127FA3CAFCB3AB007FB7FCB8FCA26C16E02C457BC437>I<190E193E19 FE18011803A21807A2180FA2181FA2183F183B187B187318F318E3170118C31703188317 071803170F171EA2173CA21778A217F0EE01E0A2EE03C0A2DC07807F160F1700161E043E 7F163C167C5E5E15014B5A5E15074B5A041FB67EED1F7F4BB7FCA25D92B8FC03F0C8FC14 014A48824A5A140F00305C007049C9127F4A8300F8137E6C5B6C48488326FF87F0043F13 3001FFF0F8F04AEFFFE04A7013C04A188091CAEBFE006C48EF0FF86C48EF07C06C4894C8 FCEA07E04C4D7DC750>65 DI<031FB512C00203B7FC021F16E091B812F8010317FE010F717E9028 3FE07FC03F80D9FE00020080D801F8041F7FD803E04A01077F48481601000F716C7E4848 717E003F02FF151F007F180F90C7707E00FE92C8FC488400F01A80008084C75AA24B81A4 14035DA21B00A24A5AA24F5AA24A5A621903624A5A4F5AA24B4B5A023F5F191F4B5E027F 4CC7FC197E92C9127C4A5E4E5A4A4B5A01014C5AF01F804A033EC8FC01035E4A4A5AEF07 E00107ED1FC04A02FFC9FC010FEC07FC4AEBFFF091B612C0017F4ACAFC90B612F0481580 4802F8CBFC4891CCFC49447EC34D>68 D<031FB512F00203B77E021F16F091B812FC0103 17FF010F188090283FE07FC00F14C0D9FE00DA007F13E0D801F84A010F13F0D803E01603 4848040013F8000F187F484801FF153F003FF01FFC007F180F90C7FC00FE92C8FC481807 12F01280C74817F85DA21AF0190F020317E05DF11FC01A80193F020717004B157E61614E 5A4A484A5A4E5AF01F80063EC7FC4A4814FCEF07F0EF7FE09239C07FFF8091273FC1FFFE C8FC03C713F003CF138091267F9FFCC9FC16800380CAFC92CBFC5CA25C1301A25C1303A2 5C13075CA2130F5C131FA25C133F5C91CCFC137E137C136046497EC345>80 D83 D<027E1718D907FF17F8011F1701017F6D1503 48B5EE07F00007180FEA0FC148C6EF1FE0123CC790C913C0193FA24A17800101177FA24A EEFF001303A24A4B5A13074A150361010F16075C011F160F4A4B5AA24948153F61017F16 7F91C9FC494C5A495DA248485D4D5B1203495D00075E495FEF3F7F000F167E5B001F4C48 C7FC4C5A494A5A003F5E933807E1FEEE0FC14848EC1F81EE3F0193383E03FC167C00FF15 F8ED01F0923803E007ED07C0DB0F805B6DEB1F00153E15FC9026E001F0130F397FF007E0 9026FC0FC0153090B5C7EBFDF06C01FCEDFFE04A5E6C01E093C7FC6C90C86C5AD803F016 F8CAEA03C0454781C33E>85 D87 DII<913807FFC0027F13FC0103B67E010F15E0903A3FFC 007FF8D97FC0EB07FCD801FEC8B4FCD803F8ED3F80D807E0ED0FC04848ED07E04848ED03 F090C91201003EEE00F8007E17FC007C177C0078173C00F8173EA248171EB3B3A6006017 0C373D7BBA42>92 D102 D<12FEEAFFE0EA07F8EA00FEEB7F806D7E6D7E130F6D7EA26D7EB3AD6D7EA2 6D7E806E7E6E7EEC0FE0EC03FC913800FFE0A2913803FC00EC0FE0EC3FC04A5A4AC7FC5C 495AA2495AB3AD495AA2495A131F495A495A01FEC8FCEA07F8EAFFE048C9FC236479CA32 >I<140C141E143EA2143C147CA214F8A214F01301A2EB03E0A214C01307A2EB0F80A214 005BA2133EA2133C137CA2137813F8A2485AA25B1203A2485AA25B120FA248C7FCA2121E 123EA25AA2127812F8A41278127CA27EA2121E121FA26C7EA212077FA26C7EA212017FA2 6C7EA21378137CA2133C133EA27FA27F1480A2EB07C0A2130314E0A2EB01F0A2130014F8 A2147CA2143C143EA2141E140C176476CA27>I<126012F07EA21278127CA27EA2121E12 1FA26C7EA212077FA26C7EA212017FA26C7EA21378137CA2133C133EA27FA27F1480A2EB 07C0A2130314E0A2EB01F0A2130014F8A2147CA2143C143EA4143C147CA214F8A214F013 01A2EB03E0A214C01307A2EB0F80A214005BA2133EA2133C137CA2137813F8A2485AA25B 1203A2485AA25B120FA248C7FCA2121E123EA25AA2127812F8A25A126017647BCA27>I< 126012F0B3B3B3B3B3A81260046474CA1C>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fy cmr12 12 84 /Fy 84 128 df0 D<1618163CA2167EA216FFA24B7FA24B6C7EA29238063FE0A24B6C7EA24B6C7EA2923838 07FC153092387003FE15609238E001FF15C002016D7F5D02036E7E92C7FC4A6E7E140602 0E6E7E140C021C6E7E141802386E7E143002706E7E146002E06E7E5C01016F7F5C010370 7E91C9FC183F010683181F4983180F49831807498318034983A249707EA24848701380A2 48CBEA7FC0A20006F03FE0A248F01FF0A2001FBA12F8A24819FCA24819FEA2BCFC48477C C651>I7 D<0103B612FCA390C701F0C8FC6F5A6F5AA8913801FFF0023FEBFF80903A01FF3FDFF0D9 07F0EBC1FCD91FC0EBC07FD93F00EC1F8001FEED0FE048486F7E48486F7E48486F7E4848 6F7E001F834982003F1880007F18C0A249163F00FF18E0A8007F18C06D167FA2003F1880 001F18006D5E000F5F6C6C4B5A6C6C4B5A6C6C4B5A6C6C4B5A013FED1F80D91FC0027FC7 FCD907F0EBC1FCD901FFEBDFF0D9003FB51280020101F0C8FC9138003FC0A84B7E4B7E01 03B612FCA33B447BC346>I<9239FFC001FC020F9038F80FFF913B3F803E3F03C0913BFC 00077E07E0D903F890390FFC0FF0494890383FF81F4948EB7FF0495A494814E049C7FCF0 0FE04991393FC0038049021F90C7FCAFB912F0A3C648C7D81FC0C7FCB3B2486CEC3FF000 7FD9FC0FB512E0A33C467EC539>11 D<4AB4FC020F13E091387F80F8903901FC001C4948 7FD907E0130F4948137F011FECFF80495A49C7FCA25B49EC7F00163E93C7FCACEE3F80B8 FCA3C648C7FC167F163FB3B0486CEC7FC0007FD9FC1FB5FCA330467EC536>I<913801FF C0020FEBFB8091387F803F903801FC00494813FFEB07E0EB1FC0A2495A49C7FC167F4914 3F5BAFB8FCA3C648C7123FB3B2486CEC7FC0007FD9FC1FB5FCA330467EC536>II22 D<121EEA7F80EAFFC0A9EA7F80 ACEA3F00AB121EAC120CA5C7FCAA121EEA7F80A2EAFFC0A4EA7F80A2EA1E000A4778C61B >33 D<001EEB03C0397F800FF000FF131F01C013F8A201E013FCA3007F130F391E6003CC 0000EB000CA401E0131C491318A3000114384913300003147090C712604814E0000614C0 000E130148EB038048EB070048130E0060130C1E1D7DC431>I<043014C00478497EA204 F81303A24C5CA203011407A24C5CA20303140FA24C91C7FCA203075CA24C131EA2030F14 3EA293C7123CA24B147CA2031E1478A2033E14F8A2033C5CA2037C1301007FBA12F8BB12 FCA26C19F8C72801F00007C0C7FC4B5CA30203140FA24B91C8FCA402075CA24B131EA302 0F143E007FBA12F8BB12FCA26C19F8C7003EC700F8C8FC023C5CA2027C1301A202785CA2 02F81303A24A5CA201011407A24A5CA20103140FA24A91C9FCA201075CA24A131EA2010F 143EA291C7123CA249147CA2011E1478A2010C143046587BC451>I<121EEA7F8012FF13 C0A213E0A3127FEA1E601200A413E013C0A312011380120313005A1206120E5A5A5A1260 0B1D78C41B>39 D<140C141C1438147014E0EB01C01303EB0780EB0F00A2131E5BA25B13 F85B12015B1203A2485AA3485AA348C7FCA35AA2123EA2127EA4127CA312FCB3A2127CA3 127EA4123EA2123FA27EA36C7EA36C7EA36C7EA212017F12007F13787FA27F7FA2EB0780 EB03C01301EB00E014701438141C140C166476CA26>I<12C07E12707E7E7E120F6C7E6C 7EA26C7E6C7EA21378137C133C133E131E131FA2EB0F80A3EB07C0A3EB03E0A314F0A213 01A214F8A41300A314FCB3A214F8A31301A414F0A21303A214E0A3EB07C0A3EB0F80A3EB 1F00A2131E133E133C137C13785BA2485A485AA2485A48C7FC120E5A5A5A5A5A16647BCA 26>I<16C04B7EB3AB007FBAFCBB1280A26C1900C8D801E0C9FCB3AB6F5A41407BB84C> 43 D<121EEA7F8012FF13C0A213E0A3127FEA1E601200A413E013C0A312011380120313 005A1206120E5A5A5A12600B1D78891B>II<121EEA7F80A2EAFF C0A4EA7F80A2EA1E000A0A78891B>I<14FF010713E090381F81F890383E007C01FC133F 4848EB1F8049130F4848EB07C04848EB03E0A2000F15F0491301001F15F8A2003F15FCA3 90C8FC4815FEA54815FFB3A46C15FEA56D1301003F15FCA3001F15F8A26C6CEB03F0A36C 6CEB07E0000315C06D130F6C6CEB1F806C6CEB3F00013E137C90381F81F8903807FFE001 0090C7FC28447CC131>48 D<143014F013011303131F13FFB5FC13E713071200B3B3B049 7E497E007FB6FCA3204278C131>II< 49B4FC010F13E0013F13FC9038FE01FE3A01F0007F80D803C0EB3FC048C7EA1FE0120EED 0FF0EA0FE0486C14F8A215077F5BA26C48130FEA03C0C813F0A3ED1FE0A2ED3FC01680ED 7F0015FE4A5AEC03F0EC1FC0D90FFFC7FC15F090380001FCEC007FED3F80ED1FC0ED0FE0 16F0ED07F816FC150316FEA2150116FFA3121EEA7F80487EA416FE491303A2007EC713FC 00701407003015F80038140F6C15F06CEC1FE06C6CEB3FC0D803E0EB7F803A01FE01FE00 39007FFFF8010F13E0010190C7FC28447CC131>II<000615C0D807C0130701 FCEB7F8090B612005D5D5D15E0158026063FFCC7FC90C9FCAE14FF010713C090381F01F0 90383800FC01F0137ED807C07F49EB1F8016C090C7120F000615E0C8EA07F0A316F81503 A216FCA5123E127F487EA416F890C712075A006015F0A20070140F003015E00038EC1FC0 7E001EEC3F806CEC7F006C6C13FE6C6C485A3901F807F039007FFFE0011F90C7FCEB07F8 26447BC131>II<121CA2EA1F8090B712C0A3481680 A217005E0038C8120C0030151C00705D0060153016705E5E4814014B5A4BC7FCC8120615 0E5D151815385D156015E04A5AA24A5A140792C8FC5CA25C141E143EA2147E147CA214FC A21301A3495AA41307A6130FAA6D5AEB01C02A457BC231>I<14FF010713E0011F13F890 387F00FE01FC133FD801F0EB1F804848EB0FC049EB07E00007EC03F048481301A290C713 F8481400A47FA26D130116F07F6C6CEB03E013FC6C6CEB07C09039FF800F806C9038C01F 006CEBF03EECF87839007FFEF090383FFFC07F01077F6D13F8497F90381E7FFFD97C1F13 80496C13C02601E00313E048486C13F000079038007FF84848EB3FFC48C7120F003EEC07 FE150148140016FF167F48153FA2161FA56C151E007C153EA2007E153C003E157C6C15F8 6DEB01F06C6CEB03E06C6CEB07C0D803F8EB1F80C6B4EBFF0090383FFFFC010F13F00101 138028447CC131>I<14FF010713E0011F13F890387F80FC9038FC007E48487F4848EB1F 804848EB0FC0000FEC07E0485AED03F0485A16F8007F140190C713FCA25AA216FE1500A5 16FFA46C5CA36C7E5D121F7F000F5C6C6C130E150C6C6C131C6C6C5BD8007C5B90383F01 E090390FFF80FE903801FE0090C8FC150116FCA4ED03F8A216F0D80F801307486C14E048 6C130F16C0ED1F80A249EB3F0049137E001EC75A001C495A000F495A3907E01FE06CB512 80C649C7FCEB1FF028447CC131>I<121EEA7F80A2EAFFC0A4EA7F80A2EA1E00C7FCB3A5 121EEA7F80A2EAFFC0A4EA7F80A2EA1E000A2B78AA1B>I<121EEA7F80A2EAFFC0A4EA7F 80A2EA1E00C7FCB3A5121E127FEAFF80A213C0A4127F121E1200A512011380A312031300 5A1206120E120C121C5A5A12600A3E78AA1B>I<007FBAFCBB1280A26C1900CEFCB0007F BAFCBB1280A26C190041187BA44C>61 D<16C04B7EA34B7EA34B7EA34B7EA3ED19FEA3ED 30FFA203707FED607FA203E07FEDC03FA2020180ED801FA2DA03007F160FA20206801607 A24A6D7EA34A6D7EA34A6D7EA20270810260147FA202E08191B7FCA249820280C7121FA2 49C87F170FA20106821707A2496F7EA3496F7EA3496F7EA201788313F8486C83D80FFF03 037FB500E0027FEBFFC0A342477DC649>65 DIIIIIIII<010FB512FEA3D9000313806E130080B3B3AB12 3F487E487EA44A5A13801300006C495A00705C6C13076C5C6C495A6CEB1F802603E07FC7 FC3800FFFCEB1FE027467BC332>I IIIIII82 D<49B41303010FEBE007013F13F89039FE00FE0FD801F8 131FD807E0EB079F49EB03DF48486DB4FC48C8FC4881003E81127E82127C00FC81A282A3 7E82A27EA26C6C91C7FC7F7FEA3FF813FE381FFFE06C13FE6CEBFFE06C14FC6C14FF6C15 C0013F14F0010F80010180D9001F7F14019138001FFF03031380816F13C0167F163F161F 17E000C0150FA31607A37EA36C16C0160F7E17806C151F6C16006C5D6D147ED8FBC05CD8 F9F0495AD8F07C495A90393FC00FE0D8E00FB51280010149C7FC39C0003FF02B487BC536 >I<003FB912F8A3903BF0001FF8001F01806D481303003EC7150048187C0078183CA200 70181CA30060180CA5481806A5C81600B3B3A54B7EED7FFE49B77EA33F447DC346>II87 D89 D91 D<01C01318000114384848137048C712E0000EEB01C0000C1480001C130300 18140000385B003013060070130E0060130CA300E0131C481318A400CFEB19E039FFC01F F801E013FCA3007F130FA2003F130701C013F8390F0001E01E1D71C431>II97 DII<167FED3FFFA3150181 82B3EC7F80903803FFF090380FC07C90383F000E017E1307496D5AD803F87F48487F5B00 0F81485AA2485AA2127FA290C8FC5AAB7E7FA2123FA26C7EA2000F5D7F6C6C5B00035C6C 6C9038077F806C6C010E13C0013F011C13FE90380FC0F8903803FFE09026007F0013002F 467DC436>IIIIII<143C14FFA2491380 A46D1300A2143C91C7FCADEC7F80EB3FFFA31300147F143FB3B3AA123E127F39FF807F00 A2147EA25C6C485A383C01F06C485A3807FF80D801FEC7FC195785C21E>IIII<3901FC01FE00FF903807FF C091381E07F091383801F8000701707F0003EBE0002601FDC07F5C01FF147F91C7FCA25B A35BB3A8486CECFF80B5D8F83F13FEA32F2C7DAB36>II<3901FC03FC00FF90380FFF8091383C07E091387001F83A07FDE000FE0003 0180137FD801FFEC3F8091C7EA1FC04915E049140F17F0160717F8160317FCA3EE01FEAB EE03FCA3EE07F8A217F0160F6D15E0EE1FC06D143F17806EEB7E00D9FDC05B9039FCF003 F891383C0FE091381FFF80DA03FCC7FC91C9FCAE487EB512F8A32F3F7DAB36>I<91387F 8003903903FFE00790380FE07890393F801C0F90387E000E496D5AD803F8EB039F0007EC 01BF4914FF48487F121F5B003F81A2485AA348C8FCAB6C7EA3123F7F121F6D5C120F6D5B 12076C6C5B6C6C497E6C6C130E013F131C90380FC0F8903803FFE09038007F0091C7FCAE EEFF80033F13FEA32F3F7DAB33>I<3903F803F000FFEB1FFCEC3C3EEC707F0007EBE0FF 3803F9C000015B13FBEC007E153C01FF13005BA45BB3A748B4FCB512FEA3202C7DAB26> I<90383FE0183901FFFC383907E01F78390F0003F8001E1301481300007C1478127800F8 1438A21518A27EA27E6C6C13006C7E13FC383FFFE06C13FC6C13FF6C14C06C14E0C614F0 011F13F81300EC0FFC140300C0EB01FE1400157E7E153EA27EA36C143C6C147C15786C14 F86CEB01F039F38003E039F1F00F8039E07FFE0038C00FF01F2E7DAC26>I<1306A5130E A4131EA3133E137EA213FE12011207001FB512F0B6FCA2C648C7FCB3A4150CAA017E131C 017F1318A26D133890381F8030ECC070903807E0E0903801FFC09038007F001E3E7EBC26 >III< B500E0B539E03FFF80A30007903C000FFE000FFC00D803FCD903F8EB03F8F001E0120103 015D6D80000060A26D6E13036DD9037E91C7FCA20280017F5B013FD9063F1306A2D91FC0 6E5AED0C1FA2D90FE06E5AED180FA2D907F06E5AED3007A2D903F86E5AED6003A2902601 FCE06D5AEDC00117FCD900FFECFD80ED800017FF027F92C8FC92C77EA26E147E023E143E A2021E143C021C141CA2412C7EAA46>III<003FB612E0A29038 C0003F90C713C0003CEC7F800038ECFF00A20030495A0070495AA24A5A0060495AA24A5A 4A5AA2C7485A4AC7FC5B5C495A13075C495A131F4A1360495A495AA249C712C0485AA248 5A485A1501485A48481303A24848EB07804848131F00FF14FF90B6FCA2232B7DAA2B>I< 001EEB0780007FEB0FE039FF801FF0EBC03FA4EB801F397F000FE0001EEB07801C0A76C2 31>127 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fz cmcsc10 12 27 /Fz 27 122 df<1638167CA316FEA34B7EA24B7FA34B7F167FA2030E7F163FA24B6C7EA2 033C7FED380FA203787FED7007A203E07F1603A24A486C7EA20203814B7EA202078192C7 127FA2020E81173FA24A6E7EA2023C810238140FA2027FB67EA302E0C7EA07FE17030101 824A80A20103834A80A249C97F187FA2010E707EA2011E83181F133E85137E48B4830007 01C0ED7FFFB500FC021FB512FEA347477CC651>65 D67 D72 DI78 D80 D82 D<157015F8A34A7EA24A 7EA34A7E81A291380E3F80A2021E7FEC1C1FA24A6C7EA34A6C7EA202F07FECE003A24948 6C7EA349486C7EA201078091C77EA249B67EA24981011CC7121FA2013C810138140FA249 6E7EA201F081491403120183486C140100074B7ED81FF84A7EB5027F13F8A335357CB43D >97 DI<4AB4EB0180021FEBF00391 B5EAFC0701039038007E0FD907F8EB0F9FD91FE0EB03DF4948EB01FF01FFC8FC4848157F 4848153FA24848151F4848150F121F491507123F5BA2007F1603A3484892C7FCAB6C7EEF 0380A2123FA27F001F16076D1600000F5E6C6C150E6C6C151E171C6C6C153C6C6C5DD93F C05C6D6CEB03E0D907F8495A902703FF807FC7FC0100EBFFFC021F13F00201138031357B B33B>IIIIIII108 DIIII 114 D<90390FF0018090387FFE0348B512873907F00FEF390FC001FF48C7FC003E143F15 1F5A150F5A1507A36C1403A27E6C91C7FC6C7E7FEA3FF8EBFF806C13FC6CEBFFC06C14F0 6C80C614FE011F7F01031480D9001F13C014019138003FE0151F150FED07F0150312E015 01A37EA216E06C1403A26CEC07C06CEC0F806C6CEB1F0001E0133ED8FBFE13FC00F0B55A D8E01F13E0D8C00390C7FC24357BB32E>I<007FB812C0A3903A8007FC003F277E0003F8 130F007C16070078160300701601A200F017E0A2481600A6C71600B3AA4A7E4A7E010FB5 12FEA333327CB13B>II119 D121 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: FA cmcsc10 10 42 /FA 42 128 df16 D<133C137EA213FE1201EA03FC13F0EA07E0EA0FC0EA1F80EA1E005A5A5A12C00F0F6DB9 2E>19 D<017F0160903807F0062701FFE0E090381FFE0E260780F99138780F9E260E001F 9138E001FE480107903901C0007E4801034948133E007815070070010191C7121E00F001 0049140EA3036015066C82A26C02006D13006C82007F6F7E01C015FCD83FFE913803FFE0 D9FFE015FE6C01F86DEBFF80000701FE6D6C13E06C6D6E13F0C66E010F13F8010F6D0100 13FC0100160FDA0FE0EC00FE0207167E6E6C153F0201161FA200C0150C0200160FA36C15 0E03E0150E6C0101010F141EA26CD903C06D133C6CD907806D1378B4D90F0001F013F026 F3E01E91383E01E026E0FFF890390E0FFF8026C01FE090390C01FE00402D7BAB4A>25 D<1430147014E0EB03C0EB0780EB0F00130E131E5B5B13F85B485AA2485AA212075B120F 90C7FC5AA2121E123EA3123C127CA5127812F8B01278127CA5123C123EA3121E121FA27E 7F12077F1203A26C7EA26C7E7F13787F7F130E130FEB0780EB03C0EB00E0147014301452 77BD24>40 D<12C07E1270123C7E7E7E7F6C7E6C7E7F12001378A27FA2133E131E131F7F 1480A2130714C0A3130314E0A5130114F0B014E01303A514C01307A31480130FA214005B 131E133E133CA25BA25B12015B485A485A90C7FC5A121E5A12705A5A14527ABD24>I<12 1C127FEAFF80A213C0A3127F121C1200A412011380A2120313005A1206120E5A5A5A1260 0A1977881B>44 DI<121C127FEAFF80A5EA7F00121C09097788 1B>I48 D51 D<00061406D80780131E9038F8 01FC90B5FC5D5D15C05D4AC7FC38067FF090C9FCABEB03FC90381FFF8090387C07E09038 E001F03907C000F8497F90C7127E0006147FC8EA3F80A216C0151FA216E0A4123E127F48 7EA490C713C048143F126016800070147F6C150015FE6C5C000F495A39078007F03903F0 1FE06CB512806C6C48C7FCEB0FF0233A7BB72E>53 D 56 DI<150EA3151FA24B7EA34B7EA3EDDFE0A202017F158F A29138030FF81507A202067F1503020E7FEC0C01A2021C7FEC1800A24A80167FA24A6D7E A202E0804A131FA2494880160FA249B67EA249810106C71203A249811601A2498182A249 6F7EA20170820160153F13E06D821203D80FFCED7FF8B56C010FB512E0A33B3C7CBB44> 65 D67 DI 70 DI73 D77 DI<003FB8 12FCA3D9C001EB800390C790C7FC007C173E0078171E0070170EA300601706A400E01707 481703A4C81500B3B0020313C0010FB612F0A338397CB841>84 DI<1407A24A7EA34A7EA3EC37E0A2EC77F01463A2ECC1F8A20101 7F1480A2903803007EA301067FA2010E80010C131FA2496D7EA2013FB57EA29038300007 496D7EA3496D7EA200018149130012036D801207D81FE0903801FF80D8FFF8010F13F8A2 2D2C7DAB33>97 DI<91383FC006903901FFF80E90390FE03E1E90381F0007017EEB03BE01F8 EB01FE484813004848147E0007153E485A001F151E5B003F150E90C8FC5A1606A212FE16 00AA007F1506A37E6D140E001F150C7F000F151C6C6C1418000315386C6C14706C6C14E0 017EEB01C0011FEB078090390FE03E00903801FFF89038003FC0272D7BAB31>III<91383FE003903901FFF807903907E01E0F90391F0007 8F017EEB01DF496DB4FC484880484880484880485A001F815B003F8190C8FC5A82A212FE 93C7FCA892383FFFF8A2007F02001380EE3F00A27E7F121F7F120F6C7E6C7E6C6C5C6C7E 017E5C011FEB01CF903907E00F87903901FFFE039026003FF0C7FC2D2D7BAB35>103 DII< B512E0A2D807F8C8FC6C5AB3A61660A416C0A31501A21503A21507ED1F80486C13FFB7FC A2232B7CAA2B>108 DIII114 D<017F13603901FFE0E0380780F9380E001F48130748130312780070130100F01300A315 607EA26C14007E127F13C0EA3FFEEBFFE06C13F8000713FE6C7FC61480010F13C01300EC 0FE01407EC03F01401A212C01400A37E15E06C1301A26CEB03C06CEB0780B4EB0F0038F3 E01E38E0FFF838C01FE01C2D7BAB26>I<007FB712C0A23A7E003FC00F007890381F8003 007015011600126000E016E0A2481660A5C71500B3A8EC7FE0011FB57EA22B2B7DAA31> II< B56CEB3FFEA2D80FFCC7EA0FF06C48EC07E00003ED03C01780000116006D5C00001506A2 017E5CA2017F141C6D141880011F5CA26D6C5BA28001075CA26D6C485AA2ECF803010191 C7FCA2903800FC06A2ECFE0EEC7E0C147F6E5AA2EC1FB0A215F06E5AA26E5AA36E5AA22F 2C7EAA33>I121 D<003C131E007F137F481480EB80FFA3EB007F6C1400003C131E190976B72E>127 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: FB cmr10 10 75 /FB 75 128 df12 D<133C137EA213FE1201EA03FC13F0EA07E0EA0F C0EA1F80EA1E005A5A5A12C00F0F6FB92A>19 D<001C131C007F137F39FF80FF80A26D13 C0A3007F137F001C131C00001300A40001130101801380A20003130301001300485B0006 1306000E130E485B485B485B006013601A197DB92A>34 D<146014E0EB01C0EB0380EB07 00130E131E5B5BA25B485AA2485AA212075B120F90C7FCA25A121EA2123EA35AA65AB212 7CA67EA3121EA2121F7EA27F12077F1203A26C7EA26C7E1378A27F7F130E7FEB0380EB01 C0EB00E01460135278BD20>40 D<12C07E12707E7E7E120F6C7E6C7EA26C7E6C7EA21378 A2137C133C133E131EA2131F7FA21480A3EB07C0A6EB03E0B2EB07C0A6EB0F80A31400A2 5B131EA2133E133C137C1378A25BA2485A485AA2485A48C7FC120E5A5A5A5A5A13527CBD 20>I<121C127FEAFF80A213C0A3127F121C1200A412011380A2120313005A1206120E5A 5A5A12600A19798817>44 DI<121C127FEAFF80A5EA7F00121C 0909798817>I48 DII I<1538A2157815F8A2140114031407A2140F141F141B14331473146314C313011483EB03 0313071306130C131C131813301370136013C01201EA038013005A120E120C5A12381230 5A12E0B712F8A3C73803F800AB4A7E0103B512F8A325397EB82A>I<0006140CD8078013 3C9038F003F890B5FC5D5D158092C7FC14FC38067FE090C9FCABEB07F8EB3FFE9038780F 803907E007E090388003F0496C7E12066E7EC87EA28181A21680A4123E127F487EA490C7 1300485C12E000605C12700030495A00385C6C1303001E495A6C6C485A3907E03F800001 B5C7FC38007FFCEB1FE0213A7CB72A>II<12301238 123E003FB612E0A316C05A168016000070C712060060140E5D151800E01438485C5D5DC7 12014A5A92C7FC5C140E140C141C5CA25CA214F0495AA21303A25C1307A2130FA3495AA3 133FA5137FA96DC8FC131E233B7BB82A>III<121C127FEAFF80A5EA7F00121CC7FCB2121C127FEAFF80A5EA7F00121C0924 79A317>I<121C127FEAFF80A5EA7F00121CC7FCB2121C127F5A1380A4127F121D1201A4 12031300A25A1206A2120E5A121812385A1260093479A317>I<1538A3157CA315FEA34A 7EA34A6C7EA202077FEC063FA2020E7FEC0C1FA2021C7FEC180FA202387FEC3007A20270 7FEC6003A202C07F1501A2D901807F81A249C77F167FA20106810107B6FCA24981010CC7 121FA2496E7EA3496E7EA3496E7EA213E0707E1201486C81D80FFC02071380B56C90B512 FEA3373C7DBB3E>65 DI<913A01FF800180020FEBE003027F13F890 3A01FF807E07903A03FC000F0FD90FF0EB039F4948EB01DFD93F80EB00FF49C8127F01FE 153F12014848151F4848150FA248481507A2485A1703123F5B007F1601A35B00FF93C7FC AD127F6DED0180A3123F7F001F160318006C7E5F6C7E17066C6C150E6C6C5D0000161801 7F15386D6C5CD91FE05C6D6CEB03C0D903FCEB0F80902701FF803FC7FC9039007FFFFC02 0F13F002011380313D7BBA3C>IIIIIII<013FB512E0A39039001FFC00EC07F8B3B3A3123FEA7F80EAFF C0A44A5A1380D87F005B0070131F6C5C6C495A6C49C7FC380781FC3801FFF038007F8023 3B7DB82B>IIIIIII82 DI<003FB812E0A3D9C003EB001F273E0001FE130348EE01F000781600 00701770A300601730A400E01738481718A4C71600B3B0913807FF80011FB612E0A33539 7DB83C>IIII89 D<003FB7FCA39039FC0001FE01C0130349495A003EC7FC003C4A5A5E0038141F00784A5A 12704B5A5E006014FF4A90C7FCA24A5A5DC712074A5AA24A5A5D143F4A5AA24A5A92C8FC 5B495AA2495A5C130F4948EB0180A2495A5C137F495A16034890C7FC5B1203485AEE0700 485A495C001F5D48485C5E4848495A49130FB8FCA329397BB833>II<3901800180000313033907000700000E130E485B00 18131800381338003013300070137000601360A200E013E0485BA400CE13CE39FF80FF80 6D13C0A3007F137FA2393F803F80390E000E001A1974B92A>II97 DIIII<147E9038 03FF8090380FC1E0EB1F8790383F0FF0137EA213FCA23901F803C091C7FCADB512FCA3D8 01F8C7FCB3AB487E387FFFF8A31C3B7FBA19>IIIIII< EA03F012FFA3120F1203B3B3AD487EB512C0A3123A7EB917>I<2703F00FF0EB1FE000FF D93FFCEB7FF8913AF03F01E07E903BF1C01F83803F3D0FF3800FC7001F802603F70013CE 01FE14DC49D907F8EB0FC0A2495CA3495CB3A3486C496CEB1FE0B500C1B50083B5FCA340 257EA445>I<3903F00FF000FFEB3FFCECF03F9039F1C01F803A0FF3800FC03803F70013 FE496D7EA25BA35BB3A3486C497EB500C1B51280A329257EA42E>II< 3903F01FE000FFEB7FF89038F1E07E9039F3801F803A0FF7000FC0D803FEEB07E049EB03 F04914F849130116FC150016FEA3167FAA16FEA3ED01FCA26DEB03F816F06D13076DEB0F E001F614C09039F7803F009038F1E07E9038F0FFF8EC1FC091C8FCAB487EB512C0A32835 7EA42E>II<3807E01F00FFEB7FC09038E1E3E09038E387F0380FE707EA03E613EE90 38EC03E09038FC0080491300A45BB3A2487EB512F0A31C257EA421>II<1318A51338A31378A313F8 120112031207001FB5FCB6FCA2D801F8C7FCB215C0A93800FC011580EB7C03017E13006D 5AEB0FFEEB01F81A347FB220>IIII II<003FB512FCA2EB8003D83E0013F8003CEB07F0 0038EB0FE012300070EB1FC0EC3F800060137F150014FE495AA2C6485A495AA2495A495A 495AA290387F000613FEA2485A485A0007140E5B4848130C4848131CA24848133C48C712 7C48EB03FC90B5FCA21F247EA325>II<001C131C007F137F39FF 80FF80A5397F007F00001C131C190978B72A>127 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: FC cmbx12 12 57 /FC 57 123 df12 D39 D46 D48 D III<163FA25E5E5D5DA25D5D5D5D A25D92B5FCEC01F7EC03E7140715C7EC0F87EC1F07143E147E147C14F8EB01F0EB03E013 0714C0EB0F80EB1F00133E5BA25B485A485A485A120F5B48C7FC123E5A12FCB91280A5C8 000F90C7FCAC027FB61280A531417DC038>I<0007150301E0143F01FFEB07FF91B6FC5E 5E5E5E5E16804BC7FC5D15E092C8FC01C0C9FCAAEC3FF001C1B5FC01C714C001DF14F090 39FFE03FFC9138000FFE01FC6D7E01F06D13804915C0497F6C4815E0C8FC6F13F0A317F8 A4EA0F80EA3FE0487E12FF7FA317F05B5D6C4815E05B007EC74813C0123E003F4A1380D8 1FC0491300D80FF0495AD807FEEBFFFC6CB612F0C65D013F1480010F01FCC7FC010113C0 2D427BC038>I<4AB47E021F13F0027F13FC49B6FC01079038807F8090390FFC001FD93F F014C04948137F4948EBFFE048495A5A1400485A120FA248486D13C0EE7F80EE1E00003F 92C7FCA25B127FA2EC07FC91381FFF8000FF017F13E091B512F89039F9F01FFC9039FBC0 07FE9039FF8003FF17804A6C13C05B6F13E0A24915F0A317F85BA4127FA5123FA217F07F 121FA2000F4A13E0A26C6C15C06D4913806C018014006C6D485A6C9038E01FFC6DB55A01 1F5C010714C0010191C7FC9038003FF02D427BC038>I<121E121F13FC90B712FEA45A17 FC17F817F017E017C0A2481680007EC8EA3F00007C157E5E00785D15014B5A00F84A5A48 4A5A5E151FC848C7FC157E5DA24A5A14035D14074A5AA2141F5D143FA2147F5D14FFA25B A35B92C8FCA35BA55BAA6D5A6D5A6D5A2F447AC238>I II65 D IIIIIIII76 DII<923807FF C092B512FE0207ECFFC0021F15F091267FFE0013FC902601FFF0EB1FFF01070180010313 C04990C76C7FD91FFC6E6C7E49486F7E49486F7E01FF8348496F7E48496F1380A248496F 13C0A24890C96C13E0A24819F04982003F19F8A3007F19FC49177FA400FF19FEAD007F19 FC6D17FFA3003F19F8A26D5E6C19F0A26E5D6C19E0A26C6D4B13C06C19806E5D6C6D4B13 006C6D4B5A6D6C4B5A6D6C4B5A6D6C4A5B6D01C001075B6D01F0011F5B010101FE90B5C7 FC6D90B65A023F15F8020715C002004AC8FC030713C047467AC454>II<923807FFC092B512FE0207ECFFC0021F15F091267FFE0013FC902601FF F0EB1FFF010701C0010713C04990C700017F49486E7F49486F7E49486F7E49486F7E4849 6F7E48496F1380A248496F13C0A24819E091C97E4819F0A248487013F8A3007F19FCA249 177FA300FF19FEAD007F19FCA36D17FF003F19F8A3001F19F06D5EA26C19E06E01FE5B6C 912603FF8014C06C6D486D4813804B13E06C9028E01F83F00F13006C903BF01E00F81FFE 90267FF83E90387C3FFC90263FFC3C6D485AD91FFE91381EFFF0D90FFF021F5B6D01FE5D 010194C7FC6D6D6CB45A023F90B512F8020703E0130202006F1307030713C792C7EA07F8 716C130F72131F9538FF80FF96B5FC7114FEA3831AFCA27213F81AF0847213E07213C072 1300F001FC48587AC454>III<003FBA 12E0A59026FE000FEB8003D87FE09338003FF049171F90C71607A2007E1803007C1801A3 00781800A400F819F8481978A5C81700B3B3A20107B8FCA545437CC24E>II<001FB812FEA59126F8000113FC02 8015F801FCC75A494A13F04916E0495C494A13C0484816805E90C84813005F003E15FF4B 5B5F003C5C4B5B5F5D4B5BC85C4B90C7FC5D5E4B5A5C5E4A5B5C5E4A5B5C5E4A90C8FC5C 5D4A48140F5B5D495B5B4949141F5D49161E495B92C8FC49163E495A5C48177E485B4A15 FE481601484914034A140748160F4849143F91C8EAFFFC48150FB9FCA538447AC344>90 D<903801FFE0011F13FE017F6D7E48B612E03A03FE007FF84848EB1FFC6D6D7E486C6D7E A26F7FA36F7F6C5A6C5AEA00F090C7FCA40203B5FC91B6FC1307013F13F19038FFFC0100 0313E0000F1380381FFE00485A5B127F5B12FF5BA35DA26D5B6C6C5B4B13F0D83FFE013E EBFFC03A1FFF80FC7F0007EBFFF86CECE01FC66CEB8007D90FFCC9FC322F7DAD36>97 DIIIIIII<137C48 B4FC4813804813C0A24813E0A56C13C0A26C13806C1300EA007C90C7FCAAEB7FC0EA7FFF A512037EB3AFB6FCA518467CC520>IIII<90277F 8007FEEC0FFCB590263FFFC090387FFF8092B5D8F001B512E002816E4880913D87F01FFC 0FE03FF8913D8FC00FFE1F801FFC0003D99F009026FF3E007F6C019E6D013C130F02BC5D 02F86D496D7EA24A5D4A5DA34A5DB3A7B60081B60003B512FEA5572D7CAC5E>I<90397F 8007FEB590383FFF8092B512E0028114F8913987F03FFC91388F801F000390399F000FFE 6C139E14BC02F86D7E5CA25CA35CB3A7B60083B512FEA5372D7CAC3E>II<90397FC00FF8B590B57E02C314E002CF14 F89139DFC03FFC9139FF001FFE000301FCEB07FF6C496D13804A15C04A6D13E05C7013F0 A2EF7FF8A4EF3FFCACEF7FF8A318F017FFA24C13E06E15C06E5B6E4913806E4913006E49 5A9139DFC07FFC02CFB512F002C314C002C091C7FCED1FF092C9FCADB67EA536407DAC3E >II<90387F807F B53881FFE0028313F0028F13F8ED8FFC91389F1FFE000313BE6C13BC14F8A214F0ED0FFC 9138E007F8ED01E092C7FCA35CB3A5B612E0A5272D7DAC2E>I<90391FFC038090B51287 000314FF120F381FF003383FC00049133F48C7121F127E00FE140FA215077EA27F01E090 C7FC13FE387FFFF014FF6C14C015F06C14FC6C800003806C15806C7E010F14C0EB003F02 0313E0140000F0143FA26C141F150FA27EA26C15C06C141FA26DEB3F8001E0EB7F009038 F803FE90B55A00FC5CD8F03F13E026E007FEC7FC232F7CAD2C>IIII121 D<001FB71280A49026FC001F130001E0495A5B49495A90C7485A48495B123E4A5B4A5B00 3C495BA24A90C7FC4A5A4A5AC7FC4A5A495B495BA2495B499038800780491300A2495A49 48130F49481400A2485B48495B485BA248495B4890C75A48485C15034848EB1FFEB7FCA4 292C7DAB32>I E %EndDVIPSBitmapFont end %%EndProlog %%BeginSetup %%Feature: *Resolution 600dpi TeXDict begin %%PaperSize: A4 %%EndSetup %%Page: 1 1 1 0 bop 578 469 a FC(A)48 b(CHARA)m(CTERIZA)-9 b(TION)45 b(OF)50 b(QUANTUM)e(GR)m(OUPS)630 718 y FB(NICOL)909 697 y(\023)899 718 y(AS)28 b(ANDR)n(USKIEWITSCH)g(AND)h(HANS-J)2441 697 y(\177)2431 718 y(UR)n(GEN)f(SCHNEIDER)119 962 y FA(Abstra)n(ct.)41 b FB(W)-7 b(e)29 b(classify)f(p)r(oin)n(ted)g(Hopf)h (algebras)d(with)j(\014nite)g(Gelfand-Kirillo)n(v)e(dimension,)i(whic)n (h)f(are)g(do-)119 1082 y(mains,)23 b(whose)e(groups)f(of)i(group-lik)n (e)e(elemen)n(ts)i(are)e(ab)r(elian,)j(and)f(whose)f(in\014nitesimal)h (braidings)f(are)g(p)r(ositiv)n(e.)1607 1565 y Fz(Intr)n(oduction)-80 1739 y Fy(Since)40 b(the)i(app)s(earance)f(of)f(quan)m(tum)h(groups)g ([KR,)f(Sk)q(,)h(Dr)o(,)g(Ji)o(],)i(there)e(w)m(ere)h(man)m(y)f (attempts)f(to)h(de\014ne)-180 1855 y(them)f(in)m(trinsically)-8 b(.)63 b(Imp)s(ortan)m(t)40 b(descriptions)g(of)g(the)h(so-called)d ("nilp)s(oten)m(t")h(parts)i(w)m(ere)g(giv)m(en)f(b)m(y)i(Ringel)-180 1972 y([Ri)o(],)c(Lusztig)e([L2])h(and)f(Rosso)h([Ro].)56 b(Ho)m(w)m(ev)m(er,)40 b(the)d(question)g(of)f(\014nding)g(an)h (abstract)g(c)m(haracterization)e(of)-180 2088 y(the)e(quan)m(tized)g (en)m(v)m(eloping)g(algebras)f(remained)g(op)s(en.)-80 2204 y(In)j(the)h(main)e(Theorem)i(5.2)f(of)g(this)g(pap)s(er,)i(w)m(e) f(classify)f(all)e(Hopf)j(algebras)f(o)m(v)m(er)h(an)f(algebraically)e (closed)-180 2320 y(\014eld)f(of)g(c)m(haracteristic)h(0)f(whic)m(h)h (are)43 2471 y Fx(\017)42 b Fy(p)s(oin)m(ted,)c(that)f(is)g(all)e (their)h(simple)g(como)s(dules)h(are)g(one-dimensional,)f(and)h(ha)m(v) m(e)i(an)e(ab)s(elian)e(group)135 2588 y(of)d(group-lik)m(e)f(elemen)m (ts,)43 2704 y Fx(\017)42 b Fy(domains)31 b(of)h(\014nite)g (Gelfand-Kirillo)m(v)c(dimension,)j(and)43 2820 y Fx(\017)42 b Fy(ha)m(v)m(e)33 b(p)s(ositiv)m(e)f(in\014nitesimal)e(braiding)h (\(see)i(Section)g(1\).)-180 2971 y(The)j(\014rst)g(t)m(w)m(o)g (conditions)e(are)i(natural.)50 b(The)37 b(p)s(ositivit)m(y)c (condition)h(should)h(b)s(e)h(related)f(to)g(the)h(existence)g(of)-180 3087 y(a)c(real)g(in)m(v)m(olution.)-80 3203 y(In)24 b(Theorem)g(4.2,)i(w)m(e)f(describ)s(e)f(these)i(Hopf)e(algebras)f(b)m (y)i(generators)f(and)h(relations.)39 b(They)25 b(are)f(natural)f(gen-) -180 3320 y(eralizations)31 b(of)h(quan)m(tized)i(en)m(v)m(eloping)f (algebras)f(with)g(p)s(ositiv)m(e)h(parameter.)44 b(T)-8 b(o)32 b(pro)m(v)m(e)j(our)d(main)g(Theorem,)-180 3436 y(w)m(e)39 b(com)m(bine)f(the)h(lifting)c(metho)s(d)j(for)g(p)s(oin)m (ted)g(Hopf)g(algebras)g([AS1,)h(AS2,)f(AS4])h(with)f(a)g(c)m (haracterization)-180 3552 y(obtained)30 b(b)m(y)i(Rosso)g(of)e(the)i ("nilp)s(oten)m(t)d(part")i(of)f(a)h(quan)m(tized)h(en)m(v)m(eloping)f (algebra)e(in)i(terms)g(of)f(\014niteness)i(of)-180 3668 y(the)h(Gelfand-Kirillo)m(v)28 b(dimension)j([Ro].)-80 3854 y(Among)38 b(the)i(main)e(di\013erences)i(b)s(et)m(w)m(een)h(the)f (new)h(Hopf)e(algebras)f(and)i(m)m(ultiparametric)c(quan)m(tized)k(en-) -180 3970 y(v)m(eloping)i(algebras,)j(let)d(us)h(men)m(tion)f(that)h(w) m(e)h(ha)m(v)m(e)g(one)f(parameter)f(of)g(deformation)f(for)i(eac)m(h)g (connected)-180 4087 y(comp)s(onen)m(t)e(of)g(the)g(Dynkin)g(diagram)e (\(this)h(is)h(explained)f(as)i(follo)m(ws:)59 b(in)40 b(the)h("classical)e(limit",)h(one)h(ma)m(y)-180 4203 y(ha)m(v)m(e)36 b(di\013eren)m(t)f(scalar)g(m)m(ultiples)e(of)h(the)h (Skly)m(anin)g(brac)m(k)m(ets)i(in)d(the)i(di\013eren)m(t)f(connected)h (comp)s(onen)m(ts\))g(and)-180 4320 y(linking)30 b(relations,)i(see)h (\(4.12\),)f(generalizing)f(the)i(classical)e(relations)g Fw(E)2580 4335 y Fv(i)2608 4320 y Fw(F)2671 4335 y Fv(j)2730 4320 y Fx(\000)23 b Fw(F)2893 4335 y Fv(j)2930 4320 y Fw(E)3002 4335 y Fv(i)3058 4320 y Fy(=)k Fw(\016)3204 4335 y Fv(ij)3265 4320 y Fy(\()p Fw(K)3386 4335 y Fv(i)3436 4320 y Fx(\000)c Fw(K)3626 4279 y Fu(\000)p Ft(1)3619 4346 y Fv(i)3720 4320 y Fy(\).)-80 4506 y(Note)33 b(that)g(w)m(e)h(are) f(not)g(assuming)f(that)h(the)g(Hopf)g(algebras)f(ha)m(v)m(e)j(an)e Fs(a-priori)f Fy(assigned)h(Dynkin)g(diagram)-180 4622 y(as)g(in)f([W,)h(KW];)f(it)g(comes)h(from)e(our)h(h)m(yp)s(othesis,)i (and)f(here)g(is)f(where)i(w)m(e)g(rely)e(on)h(Rosso's)g(result)f ([Ro].)p -180 4745 499 4 v -53 4836 a FB(V)-7 b(ersion)27 b(of)h(Jan)n(uary)d(9)j(,)f(2002.)-180 4956 y(This)h(pap)r(er)f(is)g(a) n(v)-5 b(ailable)27 b(at)g Fr(www.mate.uncor.e)o(du/)o(an)o(dr)o(us/)o (ar)o(tic)o(ul)o(os.)o(ht)o(ml)21 b FB(and)-180 5075 y Fr(www.mathematik.u)o(ni-)o(mu)o(en)o(che)o(n.)o(de/)o Fq(\030)p Fr(h)o(ans)o(sc)o(h/)o(Pub)o(li)o(cat)o(io)o(ns)o(.ht)o(ml)o FB(.)79 b(This)43 b(w)n(ork)f(w)n(as)g(partially)h(supp)r(orted)g(b)n (y)g(AN-)-180 5195 y(PCyT,)33 b(Agencia)h(C\023)-42 b(ordoba)32 b(Ciencia,)j(CONICET,)e(the)h(Graduiertenk)n(olleg)e(of)i(the)g(Math.) 56 b(Institut)35 b(\(Univ)n(ersit\177)-42 b(at)68 b(M)r(\177)-44 b(unc)n(hen\))-180 5314 y(and)27 b(Secyt)h(\(UNC\).)1927 5437 y Fp(1)p eop %%Page: 2 2 2 1 bop -180 0 a Fp(2)884 b(NICOL)1001 -19 y(\023)991 0 y(AS)24 b(ANDR)n(USKIEWITSCH)f(AND)h(HANS-J)2419 -19 y(\177)2409 0 y(UR)n(GEN)f(SCHNEIDER)-80 203 y Fy(The)44 b(article)f(is)g(organized)g(as)h(follo)m(ws.)76 b(Section)44 b(1)f(con)m(tains)h(preliminary)d(material.)75 b(In)44 b(Section)f(2,)k(w)m(e)-180 319 y(collect)30 b(some)h(w)m(ell-kno)m(wn) h(facts)f(ab)s(out)g(quan)m(tum)h(groups,)g(and)f(giv)m(e)g(details)f (of)h(some)g(pro)s(ofs)g(when)i(they)f(are)-180 435 y(not)h(easily)f(a) m(v)-5 b(ailable)30 b(in)i(the)h(literature.)43 b(Section)33 b(3)f(con)m(tains)h(a)g(tec)m(hnical)f(result)h(on)g(the)g(coradical)e (\014ltration)-180 552 y(of)j(certain)h(Hopf)f(algebras,)h (generalizing)e(an)h(idea)g(of)h(T)-8 b(ak)m(euc)m(hi.)51 b(In)35 b(Section)g(4,)g(w)m(e)g(construct)h(a)f(new)g(family)-180 668 y(of)29 b(p)s(oin)m(ted)h(Hopf)f(algebras)g(with)h(generic)g (braiding)e(and)h(establish)h(the)g(main)e(basic)i(prop)s(erties)f(of)h (them.)42 b(The)-180 784 y(approac)m(h)31 b(is)g(similar)c(to)j([AS4)q (])g(but)i(instead)e(of)h(dimension)e(argumen)m(ts,)i(w)m(e)h(use)g (the)f(tec)m(hnical)g(results)g(on)f(the)-180 900 y(coradical)e (\014ltration)g(obtained)i(in)f(Section)h(3;)h(these)g(results)f (should)g(b)s(e)h(useful)f(also)f(for)g(other)h(classes)h(of)f(Hopf) -180 1017 y(algebras.)47 b(In)35 b(Section)f(5,)g(w)m(e)h(pro)m(v)m(e)h (our)e(main)e(Theorem.)48 b(A)34 b(k)m(ey)i(p)s(oin)m(t)d(is)h(Lemma)f (5.1,)h(whic)m(h)g(implies)e(that)-180 1133 y(a)j(wide)h(class)g(of)f (Hopf)h(algebras)f(with)g(\014nite)g(Gelfand-Kirillo)m(v)c(dimension)j (is)h(generated)i(b)m(y)f(group-lik)m(e)f(and)-180 1249 y(sk)m(ew-primitiv)m(e)d(elemen)m(ts.)-180 1503 y Fs(A)-5 b(cknow)5 b(le)-5 b(dgements.)47 b Fy(W)-8 b(e)36 b(thank)g(N.)f (Reshetikhin)h(for)f(reviving)g(our)g(in)m(terest)h(in)f(this)g (question)h(and)f(J.)h(Alev)-180 1619 y(for)k(in)m(teresting)g(con)m(v) m(ersations.)67 b(This)41 b(pap)s(er)f(w)m(as)h(b)s(egun)g(during)f (visits)f(to)h(the)h(MSRI,)g(in)e(the)i(framew)m(ork)-180 1735 y(of)h(the)g(full-y)m(ear)f(Program)g(on)h(Noncomm)m(utativ)m(e)f (Algebra)h(\(August)g(1999)f(-)h(Ma)m(y)h(2000\).)71 b(W)-8 b(e)43 b(thank)f(the)-180 1852 y(organizers)d(for)f(the)i(kind)f (in)m(vitation)e(and)i(the)g(MSRI)h(for)e(the)i(excellen)m(t)f(w)m (orking)g(conditions.)63 b(P)m(art)39 b(of)f(the)-180 1968 y(w)m(ork)32 b(of)f(the)h(\014rst)h(author)e(w)m(as)h(done)g (during)f(a)g(visit)g(to)g(the)h(Univ)m(ersit)m(y)g(of)g(Reims)e (\(Octob)s(er)i(2001)e(-)h(Jan)m(uary)-180 2084 y(2002\);)h(he)h(is)f (v)m(ery)i(grateful)d(to)h(J.)h(Alev)g(for)f(his)g(kind)h(hospitalit)m (y)-8 b(.)1539 2419 y(1.)49 b Fz(Preliminaries)-180 2593 y FC(Notation.)f Fy(Let)30 b Fo(|)16 b Fy(b)s(e)31 b(an)f (algebraically)d(closed)k(\014eld)f(of)g(c)m(haracteristic)g(0.)43 b(Our)30 b(references)i(are)f([M],)g([Sw)q(])f(for)-180 2709 y(Hopf)37 b(algebras;)j([KL],)e(for)f(gro)m(wth)h(of)f(algebras)g (and)h(Gelfand-Kirillo)m(v)32 b(dimension;)39 b(and)f([AS5])f(for)g(p)s (oin)m(ted)-180 2825 y(Hopf)27 b(algebras.)41 b(W)-8 b(e)27 b(use)h(standard)f(notation)f(for)h(Hopf)f(algebras:)40 b(\001,)29 b Fx(S)7 b Fy(,)29 b Fw(\017)p Fy(,)f(denote)g(resp)s(ectiv) m(ely)g(the)f(com)m(ulti-)-180 2942 y(plication,)h(the)i(an)m(tip)s(o)s (de,)g(the)g(counit;)g(w)m(e)h(use)g(a)f(short)g(v)m(ersion)g(of)g(Sw)m (eedler's)h(notation:)41 b(\001\()p Fw(x)p Fy(\))28 b(=)g Fw(x)3690 2957 y Ft(\(1\))3801 2942 y Fx(\012)17 b Fw(x)3950 2957 y Ft(\(2\))4045 2942 y Fy(,)-180 3058 y Fw(x)33 b Fy(in)f(a)g(coalgebra)g Fw(C)7 b Fy(.)-80 3255 y(Let)41 b Fw(H)48 b Fy(b)s(e)41 b(a)f(Hopf)h(algebra)e(with)i(bijectiv)m(e)f (an)m(tip)s(o)s(de.)67 b(W)-8 b(e)42 b(denote)f(b)m(y)h Fw(G)p Fy(\()p Fw(H)8 b Fy(\))40 b(b)s(e)h(the)g(group)f(of)h(group-) -180 3371 y(lik)m(e)36 b(elemen)m(ts)i(of)e Fw(H)8 b Fy(;)39 b(and)e(b)m(y)h Fx(P)1080 3386 y Fv(g)r(;h)1181 3371 y Fy(\()p Fw(H)8 b Fy(\))36 b(the)h(space)i(of)d Fw(g)t Fy(,)i Fw(h)f Fy(sk)m(ew-primitiv)m(e)f(elemen)m(ts)h Fw(x)h Fy(of)e Fw(H)8 b Fy(,)38 b(that)f(is)f(with)-180 3487 y(\001\()p Fw(x)p Fy(\))53 b(=)g Fw(g)35 b Fx(\012)e Fw(x)f Fy(+)g Fw(x)h Fx(\012)g Fw(h)p Fy(,)51 b(where)d Fw(g)t(;)17 b(h)52 b Fx(2)h Fw(G)p Fy(\()p Fw(H)8 b Fy(\);)54 b(then)48 b Fx(P)8 b Fy(\()p Fw(H)g Fy(\))53 b(:=)f Fx(P)2630 3502 y Ft(1)p Fv(;)p Ft(1)2725 3487 y Fy(\()p Fw(H)8 b Fy(\).)87 b(The)48 b(braided)f(category)g(of)-180 3605 y(Y)-8 b(etter-Drinfeld)31 b(mo)s(dules)g(o)m(v)m(er)j Fw(H)40 b Fy(is)32 b(denoted)i(b)m(y)1813 3569 y Fv(H)1813 3630 y(H)1880 3605 y Fx(Y)8 b(D)s Fy(,)32 b Fs(cf.)43 b Fy(the)33 b(con)m(v)m(en)m(tions)i(of)d([AS5].)-80 3801 y(The)41 b(adjoin)m(t)f(represen)m(tation)h(ad)57 b(of)40 b(a)g(Hopf)h(algebra)e Fw(A)i Fy(on)g(itself)e(is)h(giv)m(en)h (b)m(y)g(ad)17 b Fw(x)p Fy(\()p Fw(y)t Fy(\))40 b(=)i Fw(x)3606 3817 y Ft(\(1\))3700 3801 y Fw(y)t Fx(S)7 b Fy(\()p Fw(x)3912 3817 y Ft(\(2\))4007 3801 y Fy(\).)-180 3923 y(If)45 b Fw(R)h Fy(is)e(a)h(braided)g(Hopf)g(algebra)f(in)1350 3887 y Fv(H)1350 3949 y(H)1417 3923 y Fx(Y)8 b(D)47 b Fy(then)f(there)g(is)e(a)h(braided)g(adjoin)m(t)f(represen)m(tation)h (ad)3794 3938 y Fv(c)3873 3923 y Fy(of)g Fw(R)-180 4040 y Fy(on)d(itself)f(giv)m(en)h(b)m(y)h(ad)739 4055 y Fv(c)774 4040 y Fw(x)p Fy(\()p Fw(y)t Fy(\))g(=)h Fw(\026)p Fy(\()p Fw(\026)28 b Fx(\012)h(S)7 b Fy(\)\(id)33 b Fx(\012)p Fw(c)p Fy(\)\(\001)d Fx(\012)f Fy(id)16 b(\)\()p Fw(x)29 b Fx(\012)g Fw(y)t Fy(\))p Fw(;)41 b Fy(where)i Fw(\026)f Fy(is)g(the)g(m)m(ultiplication)c(and)-180 4156 y Fw(c)51 b Fx(2)g Fy(End)17 b(\()p Fw(R)33 b Fx(\012)f Fw(R)q Fy(\))46 b(is)g(the)h(braiding.)82 b(If)47 b Fw(x)k Fx(2)g(P)8 b Fy(\()p Fw(R)q Fy(\))47 b(then)g(the)g(braided)f(adjoin)m(t)f (represen)m(tation)i(of)f Fw(x)g Fy(is)-180 4272 y(ad)-61 4287 y Fv(c)-26 4272 y Fw(x)p Fy(\()p Fw(y)t Fy(\))37 b(=)g Fw(\026)p Fy(\(id)32 b Fx(\000)p Fw(c)p Fy(\)\()p Fw(x)27 b Fx(\012)f Fw(y)t Fy(\))36 b(=:)i([)p Fw(x;)17 b(y)t Fy(])1370 4287 y Fv(c)1404 4272 y Fw(:)38 b Fy(The)h(elemen)m(t)f ([)p Fw(x;)17 b(y)t Fy(])2246 4287 y Fv(c)2318 4272 y Fy(de\014ned)40 b(b)m(y)f(the)g(second)g(equalit)m(y)f(for)g(an)m(y)h Fw(x)-180 4388 y Fy(and)33 b Fw(y)t Fy(,)f(regardless)i(of)e(whether)j Fw(x)e Fy(is)g(primitiv)m(e,)e(will)f(b)s(e)k(called)d(a)i(braided)g (comm)m(utator.)43 b(When)34 b Fw(A)29 b Fy(=)f Fw(R)q Fy(#)p Fw(H)8 b Fy(,)-180 4505 y(then)33 b(for)f(all)f Fw(b;)17 b(d)27 b Fx(2)h Fw(R)q Fy(,)33 b(ad)838 4520 y Ft(\()p Fv(b)p Ft(#1\))1022 4505 y Fy(\()p Fw(d)p Fy(#1\))27 b(=)g(\(ad)1567 4520 y Fv(c)1601 4505 y Fw(b)p Fy(\()p Fw(d)p Fy(\)\)#1.)-80 4723 y(If)45 b(\000)h(is)f(an)g(ab)s(elian)f (group,)k(w)m(e)f(denote)f(b)m(y)1703 4697 y Fn(b)1700 4723 y Fy(\000)f(the)h(group)f(of)h(c)m(haracters)g(of)f(\000.)83 b(If)45 b Fw(V)67 b Fy(is)45 b(a)h Fo(|)-9 b Fy(\000-)o(mo)r(dule)-180 4847 y(\(resp.,)54 b Fo(|)-9 b Fy(\000-com)o(o)s(dul)o(e\),)47 b(then)j(w)m(e)g(denote)f Fw(V)1617 4811 y Fv(\037)1720 4847 y Fy(:=)56 b Fx(f)p Fw(v)j Fx(2)c Fw(V)77 b Fy(:)56 b Fw(h:v)j Fy(=)c Fw(\037)p Fy(\()p Fw(h)p Fy(\))p Fw(v)t(;)17 b Fx(8)p Fw(h)56 b Fx(2)g Fy(\000)p Fx(g)p Fy(,)d Fw(\037)i Fx(2)3702 4822 y Fn(b)3699 4847 y Fy(\000;)i(resp.,)-180 4964 y Fw(V)-123 4979 y Fv(g)-40 4964 y Fy(:=)43 b Fx(f)p Fw(v)k Fx(2)c Fw(V)65 b Fy(:)43 b Fw(\016)t Fy(\()p Fw(v)t Fy(\))g(=)g Fw(g)31 b Fx(\012)e Fw(v)t Fx(g)p Fy(,)44 b Fw(g)i Fx(2)e Fw(G)p Fy(.)70 b(A)42 b(Y)-8 b(etter-Drinfeld)40 b(mo)s(dule)g(o)m(v)m(er)j(\000)e(is)g Fo(|)-8 b Fy(\000-)o(m)o(o)s (dul)o(e)36 b Fw(V)63 b Fy(whic)m(h)-180 5080 y(is)36 b(also)f(a)h Fo(|)-9 b Fy(\000-com)o(o)s(dul)o(e,)32 b(and)k(suc)m(h)i(that)e(eac)m(h)h(homogeneous)f(comp)s(onen)m(t)g Fw(V)2837 5095 y Fv(g)2877 5080 y Fy(,)h Fw(g)h Fx(2)c Fy(\000,)j(is)f(a)g Fo(|)-9 b Fy(\000-)o(submo)s(dule.)-180 5196 y(Th)m(us,)47 b(a)c(v)m(ector)h(space)g Fw(V)64 b Fy(pro)m(vided)43 b(with)g(a)f(direct)h(sum)g(decomp)s(osition)e Fw(V)66 b Fy(=)45 b Fx(\010)3107 5226 y Fv(g)r Fu(2)p Fv(G;\037)p Fu(2)3358 5210 y Fm(b)3356 5226 y Ft(\000)3405 5196 y Fw(V)3483 5160 y Fv(\037)3462 5221 y(g)3574 5196 y Fy(is)d(a)h(Y)-8 b(etter-)-180 5317 y(Drinfeld)31 b(mo)s(dule)g(o)m (v)m(er)i Fw(H)j Fy(=)27 b Fo(|)-8 b Fy(\000.)p eop %%Page: 3 3 3 2 bop 1010 0 a Fp(A)33 b(CHARA)n(CTERIZA)-6 b(TION)31 b(OF)i(QUANTUM)f(GR)n(OUPS)1151 b(3)-180 203 y FC(Braided)32 b(v)m(ector)g(spaces.)50 b Fy(A)28 b(braided)g(v)m(ector)i(space)f(\()p Fw(V)5 b(;)17 b(c)p Fy(\))28 b(is)g(a)g(\014nite-dimensional)d(v)m (ector)k(space)g(pro)m(vided)-180 319 y(with)40 b(an)f(isomorphism)f Fw(c)i Fy(:)g Fw(V)49 b Fx(\012)27 b Fw(V)62 b Fx(!)40 b Fw(V)48 b Fx(\012)28 b Fw(V)61 b Fy(whic)m(h)41 b(is)e(a)h(solution)e (of)h(the)i(braid)e(equation,)i(that)f(is)f(\()p Fw(c)27 b Fx(\012)-180 435 y Fy(id)16 b(\)\(id)32 b Fx(\012)p Fw(c)p Fy(\)\()p Fw(c)23 b Fx(\012)h Fy(id)16 b(\))29 b(=)g(\(id)k Fx(\012)p Fw(c)p Fy(\)\()p Fw(c)23 b Fx(\012)g Fy(id)16 b(\)\(id)32 b Fx(\012)p Fw(c)p Fy(\))p Fw(:)i Fy(Examples)g(of)f(braided)g(v)m(ector)i(spaces)g(are)f(Y)-8 b(etter-Drinfeld)-180 552 y(mo)s(dules:)42 b(if)31 b Fw(V)49 b Fx(2)529 516 y Fv(H)529 577 y(H)596 552 y Fx(Y)8 b(D)s Fy(,)32 b(then)g Fw(c)c Fy(:)g Fw(V)42 b Fx(\012)21 b Fw(V)49 b Fx(!)27 b Fw(V)42 b Fx(\012)21 b Fw(V)h Fy(,)32 b Fw(c)p Fy(\()p Fw(v)24 b Fx(\012)d Fw(w)s Fy(\))27 b(=)g Fw(v)2458 567 y Ft(\()p Fu(\000)p Ft(1\))2608 552 y Fw(:w)c Fx(\012)e Fw(v)2873 567 y Ft(\(0\))2967 552 y Fy(,)32 b(is)g(a)f(solution)f(of)i(the)g(braid)-180 668 y(equation.)-180 833 y FC(De\014nition)53 b(1.1.)c Fy(Let)e(\()p Fw(V)5 b(;)17 b(c)p Fy(\))47 b(b)s(e)g(a)g (\014nite-dimensional)d(braided)j(v)m(ector)h(space.)88 b(W)-8 b(e)47 b(shall)f(sa)m(y)i(that)e(the)-180 972 y(braiding)27 b Fw(c)h Fy(:)g Fw(V)36 b Fx(\012)15 b Fw(V)50 b Fx(!)27 b Fw(V)36 b Fx(\012)15 b Fw(V)51 b Fy(is)29 b Fs(diagonal)e Fy(if)h(there)i(exists)g(a)e(basis)h Fw(x)2481 987 y Ft(1)2521 972 y Fw(;)17 b(:)g(:)g(:)f(;)h(x)2795 987 y Fv(\022)2863 972 y Fy(of)29 b Fw(V)50 b Fy(and)29 b(non-zero)g(scalars)g Fw(q)4011 987 y Fv(ij)-180 1112 y Fy(suc)m(h)34 b(that)e Fw(c)p Fy(\()p Fw(x)386 1127 y Fv(i)437 1112 y Fx(\012)23 b Fw(x)592 1127 y Fv(j)629 1112 y Fy(\))k(=)h Fw(q)841 1127 y Fv(ij)902 1112 y Fw(x)957 1127 y Fv(j)1016 1112 y Fx(\012)22 b Fw(x)1170 1127 y Fv(i)1199 1112 y Fy(,)33 b(1)27 b Fx(\024)h Fw(i;)17 b(j)34 b Fx(\024)28 b Fw(\022)s Fy(.)44 b(The)33 b(matrix)e(\()p Fw(q)2413 1127 y Fv(ij)2474 1112 y Fy(\))h(is)g(called)g(the)h(matrix)e (of)h(the)h(braiding.)-80 1302 y(F)-8 b(urthermore,)39 b(w)m(e)g(shall)e(sa)m(y)i(that)f(a)g(diagonal)e(braiding)g(with)i (matrix)f(\()p Fw(q)2798 1317 y Fv(ij)2859 1302 y Fy(\))h(is)f Fs(inde)-5 b(c)g(omp)g(osable)36 b Fy(if)h(for)h(all)-180 1441 y Fw(i)28 b Fx(6)p Fy(=)f Fw(j)6 b Fy(,)25 b(there)f(exists)f(a)g (sequence)j Fw(i)i Fy(=)f Fw(i)1245 1456 y Ft(1)1285 1441 y Fy(,)e Fw(i)1370 1456 y Ft(2)1409 1441 y Fy(,)g(.)16 b(.)g(.)g(,)26 b Fw(i)1676 1456 y Fv(t)1734 1441 y Fy(=)h Fw(j)i Fy(of)22 b(elemen)m(ts)h(of)g Fx(f)p Fy(1)p Fw(;)17 b(:)g(:)g(:)e(;)i(\022)s Fx(g)23 b Fy(suc)m(h)h(that)f Fw(q)3391 1456 y Fv(i)3415 1464 y Fl(s)3448 1456 y Fv(;i)3492 1465 y Fl(s)p Fk(+1)3606 1441 y Fw(q)3649 1456 y Fv(i)3673 1465 y Fl(s)p Fk(+1)3784 1456 y Fv(;i)3828 1464 y Fl(s)3893 1441 y Fx(6)p Fy(=)k(1,)-180 1581 y(1)g Fx(\024)i Fw(s)e Fx(\024)h Fw(t)23 b Fx(\000)f Fy(1.)44 b(Otherwise,)33 b(w)m(e)h(sa)m(y)f(that)f(the)h(matrix)e(is)i(decomp)s(osable.)-80 1771 y(W)-8 b(e)34 b(attac)m(h)g(a)f(graph)g(to)h(a)f(diagonal)f (braiding)f(in)i(the)h(follo)m(wing)d(w)m(a)m(y)-8 b(.)48 b(The)35 b(v)m(ertices)g(of)e(the)h(graph)g(are)f(the)-180 1911 y(elemen)m(ts)28 b(of)f Fx(f)p Fy(1)p Fw(;)17 b(:)g(:)g(:)f(;)h (\022)s Fx(g)p Fy(,)28 b(and)g(there)g(is)f(an)h(edge)g(b)s(et)m(w)m (een)i Fw(i)e Fy(and)g Fw(j)33 b Fy(if)27 b(they)h(are)g(di\013eren)m (t)g(and)g Fw(q)3417 1926 y Fv(ij)3478 1911 y Fw(q)3521 1926 y Fv(j)t(i)3609 1911 y Fx(6)p Fy(=)g(1.)41 b(Th)m(us,)-180 2050 y(\\indecomp)s(osable")29 b(means)i(that)f(the)h(corresp)s(onding) g(graph)g(is)f(connected.)44 b(The)32 b(comp)s(onen)m(ts)f(of)f(the)h (matrix)-180 2190 y(are)37 b(the)h(principal)d(submatrices)i(corresp)s (onding)g(to)g(the)h(connected)h(comp)s(onen)m(ts)e(of)g(the)h(graph.) 57 b(If)37 b Fw(i)h Fy(and)f Fw(j)-180 2329 y Fy(are)31 b(v)m(ertices)h(in)e(the)h(same)g(connected)h(comp)s(onen)m(t,)f(then)h (w)m(e)f(write)g Fw(i)d Fx(\030)g Fw(j)6 b Fy(.)43 b(W)-8 b(e)31 b(shall)e(denote)j(b)m(y)f Fx(X)46 b Fy(the)31 b(set)g(of)-180 2468 y(connected)k(comp)s(onen)m(ts)f(of)e(the)i (matrix)d(\()p Fw(q)1492 2483 y Fv(ij)1553 2468 y Fy(\).)45 b(If)34 b Fw(I)i Fx(2)29 b(X)15 b Fy(,)33 b(then)h Fw(V)2362 2483 y Fv(I)2435 2468 y Fy(denotes)g(the)g(subspace)h(of)e Fw(V)54 b Fy(spanned)35 b(b)m(y)-180 2608 y Fw(x)-125 2623 y Fv(i)-96 2608 y Fy(,)d Fw(i)c Fx(2)g Fw(I)8 b Fy(.)-80 2798 y(W)-8 b(e)34 b(shall)f(sa)m(y)i(that)f(a)g(braiding)f Fw(c)h Fy(is)g Fs(generic)f Fy(if)g(it)g(is)h(diagonal)e(with)h(matrix) g(\()p Fw(q)2992 2813 y Fv(ij)3053 2798 y Fy(\))h(where)h Fw(q)3451 2813 y Fv(ii)3538 2798 y Fy(is)f(not)g(a)g(ro)s(ot)-180 2938 y(of)e(1,)g(for)h(an)m(y)g Fw(i)p Fy(.)-80 3128 y(Let)h Fo(|)16 b Fy(=)30 b Fo(C)20 b Fy(.)55 b(W)-8 b(e)34 b(shall)f(sa)m(y)i(that)g(a)f(braiding)e Fw(c)i Fy(is)g Fs(p)-5 b(ositive)33 b Fy(if)h(it)f(is)h(generic)g(with)g (matrix)e(\()p Fw(q)3460 3143 y Fv(ij)3521 3128 y Fy(\))i(where)i Fw(q)3920 3143 y Fv(ii)4006 3128 y Fy(is)-180 3267 y(a)c(p)s(ositiv)m (e)g(real)g(n)m(um)m(b)s(er,)h(for)f(all)e Fw(i)p Fy(.)-80 3458 y(W)-8 b(e)33 b(shall)f(sa)m(y)j(that)e(a)g(diagonal)e(braiding)g Fw(c)j Fy(with)f(matrix)f(\()p Fw(q)2255 3473 y Fv(ij)2315 3458 y Fy(\))i(is)e(of)h Fs(Cartan)j(typ)-5 b(e)33 b Fy(if)f Fw(q)3266 3473 y Fv(ii)3348 3458 y Fx(6)p Fy(=)d(1)k(for)g(all) e Fw(i)p Fy(,)j(and)-180 3597 y(there)42 b(are)g(in)m(tegers)g Fw(a)671 3612 y Fv(ij)773 3597 y Fy(with)f Fw(a)1055 3612 y Fv(ii)1150 3597 y Fy(=)i(2,)h(1)e Fx(\024)i Fw(i)f Fx(\024)g Fw(\022)s Fy(,)h(and)e(0)g Fx(\024)i(\000)p Fw(a)2455 3612 y Fv(ij)2559 3597 y Fw(<)f Fy(ord)16 b Fw(q)2878 3612 y Fv(ii)2972 3597 y Fy(\(whic)m(h)42 b(could)f(b)s(e)h (in\014nite\),)-180 3737 y(1)28 b Fx(\024)g Fw(i)h Fx(6)p Fy(=)e Fw(j)34 b Fx(\024)29 b Fw(\022)s Fy(,)k(suc)m(h)h(that)f Fw(q)930 3752 y Fv(ij)991 3737 y Fw(q)1034 3752 y Fv(j)t(i)1122 3737 y Fy(=)28 b Fw(q)1273 3682 y Fv(a)1310 3692 y Fl(ij)1269 3762 y Fv(ii)1402 3737 y Fy(for)k(all)f Fw(i)i Fy(and)g Fw(j)6 b Fy(.)44 b(Since)33 b(clearly)f Fw(a)2678 3752 y Fv(ij)2766 3737 y Fy(=)c(0)33 b(implies)d(that)j Fw(a)3546 3752 y Fv(j)t(i)3634 3737 y Fy(=)28 b(0)33 b(for)f(all)-180 3876 y Fw(i)c Fx(6)p Fy(=)f Fw(j)6 b Fy(,)29 b(\()p Fw(a)175 3891 y Fv(ij)235 3876 y Fy(\))e(is)g(a)g(generalized)f(Cartan)h (matrix.)40 b(This)28 b(generalizes)e(the)i(de\014nition)e(in)g([AS2,)j (p.)41 b(4].)h(In)27 b(this)g(case,)-180 4015 y(the)39 b(braiding)e(is)h(indecomp)s(osable)g(if)f(and)i(only)f(if)f(the)j (corresp)s(onding)e(Cartan)h(matrix)e(is)h(indecomp)s(osable.)-180 4155 y(W)-8 b(e)30 b(shall)e(also)h(denote)h(b)m(y)g Fx(X)45 b Fy(the)29 b(set)i(of)e(connected)i(comp)s(onen)m(ts)f(of)f (the)h(Dynkin)f(diagram)f(corresp)s(onding)h(to)-180 4294 y(the)k(matrix)e(\()p Fw(a)394 4309 y Fv(ij)455 4294 y Fy(\);)h(clearly)-8 b(,)32 b(this)g(agrees)h(with)f(the)h (previous)h(con)m(v)m(en)m(tion.)-80 4485 y(Let)f(\()p Fw(V)5 b(;)17 b(c)p Fy(\))32 b(b)s(e)h(a)g(braided)f(v)m(ector)i(space) g(of)e(Cartan)h(t)m(yp)s(e)h(with)f(generalized)f(Cartan)h(matrix)e(\() p Fw(a)3598 4500 y Fv(ij)3659 4485 y Fy(\).)44 b(W)-8 b(e)33 b(sa)m(y)-180 4624 y(that)f(\()p Fw(V)5 b(;)17 b(c)p Fy(\))33 b(is)f(of)g Fs(DJ-typ)-5 b(e)32 b Fy(\(or)h (Drinfeld-Jim)m(b)s(o)28 b(t)m(yp)s(e\))34 b(if)d(there)i(exist)g(p)s (ositiv)m(e)f(in)m(tegers)h Fw(d)3290 4639 y Ft(1)3329 4624 y Fw(;)17 b(:)g(:)g(:)f(;)h(d)3599 4639 y Fv(\022)3670 4624 y Fy(suc)m(h)34 b(that)-148 4948 y(F)-8 b(or)32 b(all)e Fw(i;)17 b(j;)50 b(d)407 4963 y Fv(i)435 4948 y Fw(a)486 4963 y Fv(ij)574 4948 y Fy(=)28 b Fw(d)729 4963 y Fv(j)765 4948 y Fw(a)816 4963 y Fv(j)t(i)909 4948 y Fy(\(th)m(us)34 b(\()p Fw(a)1251 4963 y Fv(ij)1311 4948 y Fy(\))f(is)f(symmetrizable\).)-180 4793 y(\(1.1\))-148 5271 y(F)-8 b(or)32 b(all)e Fw(I)36 b Fx(2)28 b(X)15 b Fw(;)i Fy(there)32 b(exists)i Fw(q)1026 5286 y Fv(I)1094 5271 y Fx(2)28 b Fo(|)-9 b Fy(,)27 b(whic)m(h)33 b(is)f(not)g(a)h(ro)s (ot)e(of)h(unit)m(y)-8 b(,)33 b(suc)m(h)h(that)e Fw(q)3002 5286 y Fv(ij)3091 5271 y Fy(=)27 b Fw(q)3241 5217 y Fv(d)3277 5227 y Fl(i)3304 5217 y Fv(a)3341 5227 y Fl(ij)3237 5298 y Fv(I)3433 5271 y Fy(for)32 b(all)e Fw(i;)17 b(j)34 b Fx(2)28 b Fw(I)8 b(:)-180 5116 y Fy(\(1.2\))p eop %%Page: 4 4 4 3 bop -180 0 a Fp(4)884 b(NICOL)1001 -19 y(\023)991 0 y(AS)24 b(ANDR)n(USKIEWITSCH)f(AND)h(HANS-J)2419 -19 y(\177)2409 0 y(UR)n(GEN)f(SCHNEIDER)-180 203 y Fy(In)33 b(particular,)e Fw(q)462 218 y Fv(ij)550 203 y Fy(=)d(1)k(if)g Fw(i)27 b Fx(6\030)i Fw(j)6 b Fy(.)-180 394 y FC(Nic)m(hols)33 b(algebras.)50 b Fy(Let)31 b Fw(V)49 b Fx(2)1067 357 y Fv(H)1067 419 y(H)1134 394 y Fx(Y)8 b(D)s Fy(.)43 b(A)30 b(braided)h(graded)g(Hopf)f(algebra)g Fw(R)f Fy(=)e Fx(\010)2990 409 y Fv(n)p Fu(\025)p Ft(0)3128 394 y Fw(R)q Fy(\()p Fw(n)p Fy(\))k(in)3480 357 y Fv(H)3480 419 y(H)3547 394 y Fx(Y)8 b(D)33 b Fy(is)d(called)-180 510 y(a)i Fs(Nichols)j(algebr)-5 b(a)31 b Fy(of)h Fw(V)55 b Fy(if)31 b Fo(|)13 b Fx(')28 b Fw(R)q Fy(\(0\))k(and)h Fw(V)49 b Fx(')28 b Fw(R)q Fy(\(1\))33 b(in)2054 474 y Fv(H)2054 535 y(H)2122 510 y Fx(Y)8 b(D)r Fy(,)33 b(and)-32 650 y(\(1\))42 b Fw(P)14 b Fy(\()p Fw(R)q Fy(\))27 b(=)g Fw(R)q Fy(\(1\),)-32 766 y(\(2\))42 b Fw(R)33 b Fy(is)f(generated)i(as)e(an)h(algebra)e(b)m (y)j Fw(R)q Fy(\(1\).)-80 907 y(The)k(Nic)m(hols)f(algebra)g(of)g Fw(V)59 b Fy(exists)38 b(and)g(is)f(unique)h(up)g(to)f(isomorphisms;)i (it)d(will)f(b)s(e)j(denoted)h(b)m(y)f Fj(B)p Fy(\()p Fw(V)22 b Fy(\).)-180 1023 y(It)40 b(dep)s(ends,)j(as)d(an)f(algebra)g (and)h(coalgebra,)g(only)g(on)f(the)h(underlying)f(braided)h(v)m(ector) h(space)f(\()p Fw(V)5 b(;)17 b(c)p Fy(\).)65 b(The)-180 1139 y(underlying)43 b(algebra)g(is)g(called)g(a)g Fs(quantum)i (symmetric)g(algebr)-5 b(a)43 b Fy(in)g([Ro)o(].)77 b(W)-8 b(e)44 b(shall)f(iden)m(tify)g Fw(V)65 b Fy(with)43 b(the)-180 1255 y(subspace)i(of)e(homogeneous)g(elemen)m(ts)g(of)f(degree)i(one)g (in)e Fj(B)p Fy(\()p Fw(V)21 b Fy(\).)75 b(See)44 b([AS5])f(for)g(more) f(details)g(and)h(some)-180 1372 y(historical)30 b(references.)-80 1536 y(Giv)m(en)40 b(a)g(braided)h(v)m(ector)g(space)h(of)e(an)m(y)h (of)f(the)h(t)m(yp)s(es)h(in)e(De\014nition)f(1.1,)j(w)m(e)f(will)e(sa) m(y)i(that)g(its)f(Nic)m(hols)-180 1652 y(algebra)31 b(is)i(of)f(the)h(same)f(t)m(yp)s(e.)-180 1816 y FC(Lemma)53 b(1.2.)c Fy([AS2,)g(Lemma)c(4.2])p Fs(.)82 b(L)-5 b(et)48 b Fw(V)69 b Fs(b)-5 b(e)47 b(a)g(\014nite-dimensional)e(Y)-7 b(etter-Drinfeld)47 b(mo)-5 b(dule)46 b(over)h(an)-180 1955 y(ablian)e(gr)-5 b(oup.)78 b(L)-5 b(et)47 b Fx(X)63 b Fy(=)48 b Fx(f)p Fw(I)992 1970 y Ft(1)1032 1955 y Fw(;)17 b(:)g(:)g(:)f(;)h(I)1294 1970 y Fv(N)1360 1955 y Fx(g)46 b Fs(b)-5 b(e)46 b(a)g(numer)-5 b(ation)46 b(of)f(the)i(set)f(of)g(c)-5 b(onne)g(cte)g(d)45 b(c)-5 b(omp)g(onents.)77 b(Then)-180 2095 y Fj(B)p Fy(\()p Fw(V)22 b Fy(\))53 b Fx(')h Fj(B)p Fy(\()p Fw(V)430 2110 y Fv(I)461 2119 y Fk(1)499 2095 y Fy(\))17 b Fx(\012)p 554 2119 78 4 v 16 w Fw(:)g(:)g(:)g Fx(\012)p 779 2119 V 17 w Fj(B)p Fy(\()p Fw(V)1056 2110 y Fv(I)1087 2121 y Fl(N)1148 2095 y Fy(\))49 b Fs(as)f(br)-5 b(aide)g(d)48 b(Hopf)h(algebr)-5 b(as)47 b(with)i(the)g(br)-5 b(aide)g(d)48 b(tensor)g(pr)-5 b(o)g(duct)49 b(algebr)-5 b(a)-180 2234 y(structur)g(e)36 b Fx(\012)p 231 2258 V 35 w Fs(.)3621 b Fi(\003)-180 2423 y FC(Lifting)50 b(metho)s(d)h(for)h(p)s(oin)m(ted)f(Hopf)g(algebras.)f Fy(Recall)43 b(that)h(a)h(Hopf)f(algebra)g Fw(A)h Fy(is)f(p)s(oin)m (ted)h(if)e(an)m(y)-180 2539 y(irreducible)e Fw(A)p Fy(-como)s(dule)f (is)h(one-dimensional.)69 b(That)43 b(is,)h(if)c(the)j(coradical)d Fw(A)2913 2554 y Ft(0)2995 2539 y Fy(equals)i(the)g(group)g(algebra) -180 2656 y Fo(|)-9 b Fw(G)p Fy(\()p Fw(A)p Fy(\).)-80 2820 y(Let)40 b Fw(A)g Fy(b)s(e)g(a)f(p)s(oin)m(ted)h(Hopf)f(algebra)g (let)g Fw(A)1618 2835 y Ft(0)1698 2820 y Fy(=)h Fo(|)-9 b Fw(G)p Fy(\()p Fw(A)p Fy(\))34 b Fx(\022)41 b Fw(AA)2399 2835 y Ft(1)2478 2820 y Fx(\022)g Fw(:)17 b(:)g(:)56 b Fy(b)s(e)40 b(the)g(coradical)e(\014ltration)g(and)-180 2936 y(let)k(gr)16 b Fw(A)46 b Fy(=)f Fx(\010)391 2951 y Fv(n)p Fu(\025)p Ft(0)528 2936 y Fy(gr)16 b Fw(A)p Fy(\()p Fw(n)p Fy(\))43 b(b)s(e)g(the)h(asso)s(ciated)f(graded)g (coalgebra,)h(whic)m(h)g(is)e(a)h(graded)g(Hopf)g(algebra)e([M)q(].) -180 3052 y(The)d(graded)f(pro)5 b(jection)37 b Fw(\031)j Fy(:)35 b(gr)16 b Fw(A)35 b Fx(!)g Fy(gr)16 b Fw(A)p Fy(\(0\))36 b Fx(')f Fo(|)-8 b Fw(G)p Fy(\()p Fw(A)p Fy(\))31 b(is)36 b(a)h(Hopf)g(algebra)f(map)g(and)i(a)f(retraction)f (of)g(the)-180 3169 y(inclusion.)72 b(Let)43 b Fw(R)j Fy(=)f Fx(f)p Fw(a)g Fx(2)h Fw(A)f Fy(:)g(\(id)32 b Fx(\012)p Fw(\031)t Fy(\)\001\()p Fw(a)p Fy(\))46 b(=)f Fw(a)29 b Fx(\012)h Fy(1)p Fx(g)42 b Fy(b)s(e)h(the)g(algebra)f(of)g(coin)m(v) -5 b(arian)m(ts)42 b(of)g Fw(\031)t Fy(;)48 b Fw(R)c Fy(is)e(a)-180 3303 y(braided)27 b(Hopf)g(algebra)f(in)g(the)i (category)1394 3252 y Fv(G)p Ft(\()p Fv(A)p Ft(\))1394 3334 y Fv(G)p Ft(\()p Fv(A)p Ft(\))1561 3303 y Fx(Y)8 b(D)30 b Fy(of)d(Y)-8 b(etter-Drinfeld)25 b(mo)s(dules)h(o)m(v)m(er)i Fo(|)-8 b Fw(G)p Fy(\()p Fw(A)p Fy(\))21 b(and)27 b(gr)16 b Fw(A)27 b Fy(can)h(b)s(e)-180 3434 y(reconstructed)38 b(from)d Fw(R)i Fy(and)f Fo(|)-9 b Fw(G)p Fy(\()p Fw(A)p Fy(\))30 b(as)36 b(a)g(b)s(osonization:)48 b(gr)16 b Fw(A)34 b Fx(')g Fw(R)q Fy(#)p Fo(|)-9 b Fw(G)p Fy(\()p Fw(A)p Fy(\).)48 b(Moreo)m(v)m(er,)38 b Fw(R)d Fy(=)e Fx(\010)3698 3449 y Fv(n)p Fu(\025)p Ft(0)3836 3434 y Fw(R)q Fy(\()p Fw(n)p Fy(\),)-180 3550 y(where)h Fw(R)q Fy(\()p Fw(n)p Fy(\))27 b(=)h(gr)16 b Fw(A)p Fy(\()p Fw(n)p Fy(\))22 b Fx(\\)g Fw(R)34 b Fy(is)e(a)g(graded)g(braided)g (Hopf)h(algebra.)42 b(W)-8 b(e)33 b(then)g(ha)m(v)m(e)h(sev)m(eral)f (in)m(v)-5 b(arian)m(ts)31 b(of)h(our)-180 3666 y(initial)h(p)s(oin)m (ted)k(Hopf)g(algebra)f Fw(A)p Fy(:)53 b(The)38 b(graded)f(braided)g (Hopf)g(algebra)f Fw(R)q Fy(;)j(it)d(is)h(called)f(the)h Fs(diagr)-5 b(am)36 b Fy(of)h Fw(A)p Fy(.)-180 3782 y(The)f(braided)f (v)m(ector)i(space)f(\()p Fw(V)5 b(;)17 b(c)p Fy(\),)36 b(where)g Fw(V)54 b Fy(:=)33 b Fw(R)q Fy(\(1\))f(=)g Fw(P)14 b Fy(\()p Fw(R)q Fy(\))34 b(and)i Fw(c)c Fy(:)h Fw(V)45 b Fx(\012)25 b Fw(V)53 b Fx(!)32 b Fw(V)46 b Fx(\012)24 b Fw(V)57 b Fy(is)35 b(the)h(braiding)-180 3916 y(in)-66 3865 y Fv(G)p Ft(\()p Fv(A)p Ft(\))-66 3948 y Fv(G)p Ft(\()p Fv(A)p Ft(\))101 3916 y Fx(Y)8 b(D)s Fy(.)44 b(It)33 b(will)e(b)s(e)i(called)f(the)i Fs(in\014nitesimal)f(br)-5 b(aiding)32 b Fy(of)h Fw(A)p Fy(.)45 b(The)34 b(dimension)d(of)i Fw(V)50 b Fy(=)28 b Fw(P)14 b Fy(\()p Fw(R)q Fy(\),)33 b(called)e(the)-180 4047 y Fs(r)-5 b(ank)36 b Fy(of)g Fw(A)p Fy(,)i(or)e(of)h Fw(R)q Fy(.)55 b(The)38 b(subalgebra)e Fw(R)1463 4011 y Fu(0)1523 4047 y Fy(of)g Fw(R)i Fy(generated)f(b)m(y)h Fw(R)q Fy(\(1\),)f(whic)m(h)g(is)g(the)g(Nic)m(hols)f(algebra)f(of)h Fw(V)22 b Fy(:)-180 4164 y Fw(R)-105 4127 y Fu(0)-54 4164 y Fx(')28 b Fj(B)p Fy(\()p Fw(V)22 b Fy(\).)43 b(See)34 b([AS5])e(for)g(more)g(details.)1027 4406 y(2.)49 b Fz(Nichols)38 b(algebras)f(of)h(Car)-7 b(t)g(an)39 b(type)-180 4580 y FC(Nic)m(hols)44 b(algebras)i(of)h(diagonal)e(t)m(yp)s(e.)k Fy(In)41 b(this)f(section,)i(\()p Fw(V)5 b(;)17 b(c)p Fy(\))39 b(denotes)j(a)d(\014nite-dimensional)e(braided)-180 4696 y(v)m(ector)k(space;)j(w)m(e)c(assume)g(that)f(the)h(braiding)e Fw(c)h Fy(is)g(diagonal)e(with)i(matrix)f(\()p Fw(q)2914 4711 y Fv(ij)2975 4696 y Fy(\),)j(with)e(resp)s(ect)i(to)e(a)g(basis) -180 4812 y Fw(x)-125 4827 y Ft(1)-85 4812 y Fw(;)17 b(:)g(:)g(:)f(x)145 4827 y Fv(\022)184 4812 y Fy(.)-80 4929 y(Let)32 b(\000)h(b)s(e)f(the)h(free)g(ab)s(elian)e(group)h(of)g (rank)h Fw(\022)i Fy(with)d(basis)h Fw(g)2215 4944 y Ft(1)2254 4929 y Fw(;)17 b(:)g(:)g(:)f(;)h(g)2520 4944 y Fv(\022)2558 4929 y Fy(.)43 b(W)-8 b(e)33 b(de\014ne)h(c)m(haracters) g Fw(\037)3603 4944 y Ft(1)3642 4929 y Fw(;)17 b(:)g(:)g(:)f(;)h(\037) 3922 4944 y Fv(\022)3993 4929 y Fy(of)-180 5045 y(\000)32 b(b)m(y)1329 5169 y Fw(\037)1390 5184 y Fv(i)1418 5169 y Fy(\()p Fw(g)1503 5184 y Fv(j)1539 5169 y Fy(\))c(=)f Fw(q)1751 5184 y Fv(j)t(i)1812 5169 y Fw(;)212 b Fy(1)27 b Fx(\024)h Fw(i;)17 b(j)34 b Fx(\024)28 b Fw(\022)s(:)-180 5313 y Fy(W)-8 b(e)33 b(consider)g Fw(V)54 b Fy(as)33 b(a)f(Y)-8 b(etter-Drinfeld)31 b(mo)s(dule)g(o)m(v)m(er)j Fo(|)-9 b Fy(\000)26 b(b)m(y)34 b(de\014ning)e Fw(x)2619 5328 y Fv(i)2676 5313 y Fx(2)c Fw(V)2848 5276 y Fv(\037)2892 5286 y Fl(i)2827 5337 y Fv(g)2861 5347 y Fl(i)2923 5313 y Fy(,)k(for)g(all)f Fw(i)p Fy(.)p eop %%Page: 5 5 5 4 bop 1010 0 a Fp(A)33 b(CHARA)n(CTERIZA)-6 b(TION)31 b(OF)i(QUANTUM)f(GR)n(OUPS)1151 b(5)-80 203 y Fy(W)-8 b(e)33 b(b)s(egin)e(with)i(some)f(relations)f(that)i(hold)e(in)h(an)m (y)h(Nic)m(hols)f(algebra)g(of)g(diagonal)e(t)m(yp)s(e.)-180 378 y FC(Lemma)37 b(2.1.)42 b Fs(L)-5 b(et)35 b Fw(R)h Fs(b)-5 b(e)35 b(a)f(br)-5 b(aide)g(d)34 b(Hopf)h(algebr)-5 b(a)34 b(in)1937 342 y Fh(|)-14 b Ft(\000)1937 404 y Fh(|)g Ft(\000)2022 378 y Fx(Y)8 b(D)r Fs(,)35 b(such)g(that)g Fw(V)49 b(,)-17 b Fx(!)28 b Fw(P)14 b Fy(\()p Fw(R)q Fy(\))p Fs(.)-80 518 y(\(a\).)44 b(If)34 b Fw(q)269 533 y Fv(ii)356 518 y Fs(is)h(a)g(r)-5 b(o)g(ot)35 b(of)f(1)h(of)g(or)-5 b(der)34 b Fw(N)k(>)28 b Fy(1)35 b Fs(for)f(some)g Fw(i)28 b Fx(2)g(f)p Fy(1)p Fw(;)17 b(:)g(:)g(:)f(;)h(\022)s Fx(g)p Fs(,)34 b(then)h Fw(x)2929 482 y Fv(N)2929 542 y(i)3024 518 y Fx(2)28 b Fw(P)14 b Fy(\()p Fw(R)q Fy(\))p Fs(.)-80 657 y(\(b\).)41 b(L)-5 b(et)28 b Fw(i)g Fx(6)p Fy(=)g Fw(j)33 b Fx(2)28 b(f)p Fy(1)p Fw(;)17 b(:)g(:)g(:)f(;)h(\022)s Fx(g)27 b Fs(such)g(that)h Fw(q)1501 672 y Fv(ij)1562 657 y Fw(q)1605 672 y Fv(j)t(i)1693 657 y Fy(=)g Fw(q)1844 616 y Ft(1)p Fu(\000)p Fv(r)1840 683 y(ii)1972 657 y Fs(,)g(wher)-5 b(e)27 b Fw(r)j Fs(is)d(an)g(inte)-5 b(ger)27 b(such)g(that)h Fy(0)g Fx(\024)g Fw(r)8 b Fx(\000)e Fy(1)27 b Fw(<)h Fy(ord)17 b Fw(q)4020 672 y Fv(ii)-180 797 y Fs(\(which)34 b(c)-5 b(ould)34 b(b)-5 b(e)35 b(in\014nite\).)44 b(Then)34 b Fy(\(ad)16 b Fw(x)1387 812 y Fv(i)1416 797 y Fy(\))1454 761 y Fv(r)1492 797 y Fy(\()p Fw(x)1585 812 y Fv(j)1621 797 y Fy(\))35 b Fs(is)g(primitive)f(in)h Fw(R)q Fs(.)-80 936 y(Assume)f(for)h(the)g(r)-5 b(est)35 b(of)g(the)g(L)-5 b(emma)34 b(that)h Fw(R)29 b Fy(=)e Fj(B)p Fy(\()p Fw(V)22 b Fy(\))p Fs(.)-80 1076 y(\(c\).)44 b(In)34 b(the)h(situation)g(of)g(\(a\),)f(r)-5 b(esp.)44 b(\(b\),)34 b Fw(x)1612 1039 y Fv(N)1612 1100 y(i)1708 1076 y Fy(=)27 b(0)p Fs(,)35 b(r)-5 b(esp.)44 b Fy(ad)16 b Fw(x)2344 1039 y Fv(r)2344 1100 y(i)2383 1076 y Fy(\()p Fw(x)2476 1091 y Fv(j)2513 1076 y Fy(\))27 b(=)h(0)p Fs(.)-80 1215 y(\(d\).)44 b(If)34 b Fw(R)29 b Fy(=)e Fj(B)p Fy(\()p Fw(V)22 b Fy(\))35 b Fs(is)f(an)h(inte)-5 b(gr)g(al)34 b(domain,)g(then)h Fw(q)1940 1230 y Fv(ii)2020 1215 y Fy(=)27 b(1)35 b Fs(or)g(it)g(is)f(not)h(a)g(r)-5 b(o)g(ot)35 b(of)g(1,)f(for)h(al)5 b(l)34 b Fw(i)p Fs(.)-80 1355 y(\(e\).)44 b(If)34 b Fw(i)28 b Fx(6)p Fy(=)g Fw(j)6 b Fs(,)34 b(then)h Fy(ad)832 1370 y Fv(c)867 1355 y Fy(\()p Fw(x)960 1370 y Fv(i)989 1355 y Fy(\))1027 1318 y Fv(r)1064 1355 y Fy(\()p Fw(x)1157 1370 y Fv(j)1194 1355 y Fy(\))28 b(=)g(0)34 b Fs(if)h(and)f(only)h(if)f Fy(\()p Fw(r)s Fy(\)!)2187 1370 y Fv(q)2219 1380 y Fl(ii)2288 1280 y Fn(Q)2382 1384 y Ft(0)p Fu(\024)p Fv(k)r Fu(\024)p Fv(r)r Fu(\000)p Ft(1)2710 1274 y Fn(\000)2756 1355 y Fy(1)22 b Fx(\000)h Fw(q)2974 1318 y Fv(k)2970 1379 y(ii)3022 1355 y Fw(q)3065 1370 y Fv(ij)3126 1355 y Fw(q)3169 1370 y Fv(j)t(i)3230 1274 y Fn(\001)3303 1355 y Fy(=)k(0)p Fs(.)-180 1582 y(Pr)-5 b(o)g(of.)41 b Fy(\(a\))30 b(and)g(\(b\))g(are)g (consequences)k(of)29 b(the)i(quan)m(tum)f(binomial)d(form)m(ula,)i (see)i Fs(e.)44 b(g.)e Fy([AS2,)31 b(App)s(endix])f(for)-180 1721 y(\(b\).)59 b(Then)38 b(\(c\))g(and)g(\(d\))f(follo)m(w;)i(the)f (second)h(statemen)m(t)f(in)f(\(c\))g(is)g(also)g(a)g(consequence)k(of) c(\(e\).)59 b(P)m(art)38 b(\(e\))f(is)-180 1861 y(from)31 b([Ro,)i(Lemma)e(14];)h(it)g(can)g(also)g(b)s(e)h(sho)m(wn)h(using)e (sk)m(ew-deriv)-5 b(ations)33 b(as)g(in)f([AS5,)g(Section)h(2.2].)301 b Fi(\003)-80 2078 y Fy(W)-8 b(e)39 b(no)m(w)h(recall)e(a)h(v)-5 b(ariation)36 b(of)j(a)g(w)m(ell-kno)m(wn)g(result)g(of)g(Reshetikhin)g (on)g(t)m(wisting)g([Re].)63 b(Let)40 b(\()3743 2053 y Fn(b)3731 2078 y Fw(V)21 b(;)15 b Fn(b)-53 b Fw(c)p Fy(\))39 b(b)s(e)-180 2195 y(another)33 b(braided)g(v)m(ector)h(space)g (of)f(the)h(same)f(dimension)e(as)j Fw(V)21 b Fy(,)34 b(suc)m(h)g(that)f(the)h(braiding)c Fn(b)-54 b Fw(c)33 b Fy(is)g(diagonal)d(with)-180 2311 y(matrix)h(\()t Fn(b)-59 b Fw(q)218 2326 y Fv(ij)279 2311 y Fy(\))32 b(with)g(resp)s(ect)i(to)e (a)h(basis)i Fn(b)-58 b Fw(x)1400 2326 y Ft(1)1440 2311 y Fw(;)17 b(:)g(:)g(:)i Fn(b)-58 b Fw(x)1670 2326 y Fv(\022)1709 2311 y Fy(.)44 b(W)-8 b(e)33 b(de\014ne)h(c)m(haracters)42 b Fn(b)-63 b Fw(\037)2755 2326 y Ft(1)2794 2311 y Fw(;)17 b(:)g(:)g(:)f(;)25 b Fn(b)-63 b Fw(\037)3074 2326 y Fv(\022)3145 2311 y Fy(of)32 b(\000)h(b)m(y)1337 2499 y Fn(b)-63 b Fw(\037)1390 2514 y Fv(i)1418 2499 y Fy(\()p Fw(g)1503 2514 y Fv(j)1539 2499 y Fy(\))28 b(=)j Fn(b)-59 b Fw(q)1751 2514 y Fv(j)t(i)1812 2499 y Fw(;)212 b Fy(1)27 b Fx(\024)h Fw(i;)17 b(j)34 b Fx(\024)28 b Fw(\022)s(:)-180 2703 y Fy(W)-8 b(e)33 b(consider)379 2678 y Fn(b)368 2703 y Fw(V)54 b Fy(as)33 b(a)f(Y)-8 b(etter-Drinfeld)31 b(mo)s(dule)g(o)m (v)m(er)j(\000)e(b)m(y)h(de\014ning)j Fn(b)-58 b Fw(x)2564 2718 y Fv(i)2620 2703 y Fx(2)2726 2678 y Fn(b)2714 2703 y Fw(V)2799 2667 y Fm(b)-45 b Fv(\037)2837 2677 y Fl(i)2771 2728 y Fv(g)2805 2738 y Fl(i)2867 2703 y Fy(,)33 b(for)f(all)e Fw(i)p Fy(.)-180 2879 y FC(Prop)s(osition)36 b(2.2.)41 b Fs(Assume)35 b(that)g(for)g(al)5 b(l)35 b Fw(i;)17 b(j)6 b Fs(,)34 b Fw(q)1730 2894 y Fv(ii)1810 2879 y Fy(=)e Fn(b)-59 b Fw(q)1957 2894 y Fv(ii)2044 2879 y Fs(and)-180 3090 y Fy(\(2.1\))1638 b Fw(q)1702 3105 y Fv(ij)1763 3090 y Fw(q)1806 3105 y Fv(j)t(i)1894 3090 y Fy(=)32 b Fn(b)-59 b Fw(q)2041 3105 y Fv(ij)2106 3090 y Fn(b)g Fw(q)2145 3105 y Fv(j)t(i)2206 3090 y Fw(:)-80 3300 y Fs(Then)34 b(ther)-5 b(e)35 b(exists)f(an)g Fo(N)9 b Fs(-gr)-5 b(ade)g(d)40 b(isomorphism)34 b(of)g Fo(|)-9 b Fy(\000)p Fs(-c)k(omo)f(dules)29 b Fw( )j Fy(:)27 b Fj(B)p Fy(\()p Fw(V)22 b Fy(\))28 b Fx(!)f Fj(B)p Fy(\()3220 3275 y Fn(b)3208 3300 y Fw(V)21 b Fy(\))35 b Fs(such)g(that)-180 3511 y Fy(\(2.2\))1371 b Fw( )t Fy(\()p Fw(x)1552 3526 y Fv(i)1581 3511 y Fy(\))28 b(=)i Fn(b)-58 b Fw(x)1805 3526 y Fv(i)1834 3511 y Fw(;)216 b Fy(1)27 b Fx(\024)h Fw(i)g Fx(\024)g Fw(\022)s(:)-180 3722 y Fs(L)-5 b(et)36 b Fw(\033)d Fy(:)c(\000)22 b Fx(\002)h Fy(\000)29 b Fx(!)g Fo(|)596 3686 y Fu(\002)685 3722 y Fs(b)-5 b(e)35 b(the)h(unique)f (biline)-5 b(ar)35 b(form)g(such)g(that)h Fw(\033)t Fy(\()p Fw(g)2435 3737 y Fv(i)2463 3722 y Fw(;)17 b(g)2554 3737 y Fv(j)2590 3722 y Fy(\))29 b(=)j Fn(b)-59 b Fw(q)2804 3737 y Fv(ij)2865 3722 y Fw(q)2912 3681 y Fu(\000)p Ft(1)2908 3748 y Fv(ij)3006 3722 y Fs(,)36 b(if)f Fw(i)29 b Fx(\024)h Fw(j)6 b Fs(,)35 b(and)g(is)h(e)-5 b(qual)35 b(to)-180 3862 y(1)g(otherwise;)f Fw(\033)39 b Fs(is)34 b(a)h(gr)-5 b(oup)35 b(2-c)-5 b(o)g(cycle)34 b(and)g(we)g(have,)g(for)h(al)5 b(l)35 b Fw(g)t(;)17 b(h)26 b Fx(2)i Fy(\000)p Fs(,)817 4073 y Fw( )t Fy(\()p Fw(xy)t Fy(\))f(=)g Fw(\033)t Fy(\()p Fw(g)t(;)17 b(h)p Fy(\))p Fw( )t Fy(\()p Fw(x)p Fy(\))p Fw( )t Fy(\()p Fw(y)t Fy(\))p Fw(;)215 b(x)28 b Fx(2)g Fj(B)p Fy(\()p Fw(V)21 b Fy(\))2537 4088 y Fv(g)2577 4073 y Fw(;)117 b(y)30 b Fx(2)f Fj(B)p Fy(\()p Fw(V)21 b Fy(\))3136 4088 y Fv(h)3181 4073 y Fy(;)-3388 b(\(2.3\))684 4241 y Fw( )t Fy(\([)p Fw(x;)17 b(y)t Fy(])994 4256 y Fv(c)1028 4241 y Fy(\))28 b(=)f Fw(\033)t Fy(\()p Fw(g)t(;)17 b(h)p Fy(\)[)p Fw( )t Fy(\()p Fw(x)p Fy(\))p Fw(;)g( )t Fy(\()p Fw(y)t Fy(\)])1974 4256 y Fv(c)2007 4241 y Fw(;)216 b(x)28 b Fx(2)g Fw(V)2506 4200 y Fv(\037)2484 4266 y(g)2554 4241 y Fw(;)116 b(y)31 b Fx(2)d Fj(B)p Fy(\()p Fw(V)22 b Fy(\))3113 4194 y Fv(\021)3113 4269 y(h)3157 4241 y Fw(:)-3364 b Fy(\(2.4\))-180 4468 y Fs(Pr)-5 b(o)g(of.)41 b Fy(See)34 b([AS5,)e(Prop.)44 b(3.9)32 b(and)h(Remark)f(3.10].)2220 b Fi(\003)-180 4695 y FC(Remark)35 b(2.3.)41 b Fy(In)32 b(the)f(situation)f(of)h(the)h(prop)s(osition,)d(w)m(e)k(sa)m(y)f(that) f Fj(B)p Fy(\()p Fw(V)21 b Fy(\))32 b(and)f Fj(B)p Fy(\()3086 4670 y Fn(b)3074 4695 y Fw(V)21 b Fy(\))32 b(are)f Fs(twist-e)-5 b(quivalent)9 b Fy(;)-180 4835 y(note)32 b(that)g Fj(B)p Fy(\()p Fw(V)22 b Fy(\))32 b(is)f(t)m(wist-equiv)-5 b(alen)m(t)32 b(to)f(a)h Fj(B)p Fy(\()1661 4810 y Fn(b)1649 4835 y Fw(V)22 b Fy(\))32 b(with)j Fn(b)-59 b Fw(q)2062 4850 y Fv(ij)2151 4835 y Fy(=)31 b Fn(b)-59 b Fw(q)2297 4850 y Fv(j)t(i)2390 4835 y Fy(for)32 b(all)e Fw(i)i Fy(and)g Fw(j)6 b Fy(,)32 b(since)h(all)d(the)i Fw(q)3617 4850 y Fv(ij)3678 4835 y Fw(q)3721 4850 y Fv(j)t(i)3782 4835 y Fy('s)h(ha)m(v)m(e)-180 4974 y(square)h(ro)s(ots)e(in)g Fo(|)-9 b Fy(.)-180 5150 y FC(Lemma)25 b(2.4.)34 b Fs(Assume)25 b(that)g(the)h(br)-5 b(aiding)24 b(with)h(matrix)g Fy(\()p Fw(q)2060 5165 y Fv(ij)2120 5150 y Fy(\))g Fs(is)g(generic)g(and)f(of)h (Cartan)g(typ)-5 b(e)25 b(with)g(gener)-5 b(alize)g(d)-180 5289 y(Cartan)35 b(matrix)f Fy(\()p Fw(a)554 5304 y Fv(ij)615 5289 y Fy(\))p Fs(.)44 b(Then)34 b Fy(\()p Fw(a)1070 5304 y Fv(ij)1131 5289 y Fy(\))h Fs(is)g(symmetrizable.)p eop %%Page: 6 6 6 5 bop -180 0 a Fp(6)884 b(NICOL)1001 -19 y(\023)991 0 y(AS)24 b(ANDR)n(USKIEWITSCH)f(AND)h(HANS-J)2419 -19 y(\177)2409 0 y(UR)n(GEN)f(SCHNEIDER)-180 203 y Fs(Pr)-5 b(o)g(of.)41 b Fy(By)c([K,)g(Ex.)55 b(2.1],)37 b(it)e(is)h(enough)h(to) e(sho)m(w)j(that)e Fw(a)2034 218 y Fv(i)2058 227 y Fk(1)2093 218 y Fv(i)2117 227 y Fk(2)2155 203 y Fw(a)2206 218 y Fv(i)2230 227 y Fk(2)2265 218 y Fv(i)2289 227 y Fk(3)2345 203 y Fw(:)17 b(:)g(:)f(a)2527 218 y Fv(i)2551 227 y Fl(t)p Fg(\000)p Fk(1)2657 218 y Fv(i)2681 226 y Fl(t)2713 203 y Fw(a)2764 218 y Fv(i)2788 226 y Fl(t)2816 218 y Fv(i)2840 227 y Fk(1)2913 203 y Fy(=)34 b Fw(a)3074 218 y Fv(i)3098 227 y Fk(2)3133 218 y Fv(i)3157 227 y Fk(1)3195 203 y Fw(a)3246 218 y Fv(i)3270 227 y Fk(3)3305 218 y Fv(i)3329 227 y Fk(2)3385 203 y Fw(:)17 b(:)g(:)f(a)3567 218 y Fv(i)3591 226 y Fl(t)3619 218 y Fv(i)3643 227 y Fl(t)p Fg(\000)p Fk(1)3753 203 y Fw(a)3804 218 y Fv(i)3828 227 y Fk(1)3863 218 y Fv(i)3887 226 y Fl(t)3955 203 y Fy(for)-180 342 y(all)30 b Fw(i)-12 357 y Ft(1)28 342 y Fw(;)17 b(i)105 357 y Ft(2)145 342 y Fw(;)g(:)g(:)g(:)e(;)i(i)396 357 y Fv(t)426 342 y Fy(.)43 b(But)494 569 y Fw(q)541 503 y Fv(a)578 513 y Fl(i)600 528 y Fk(1)635 513 y Fl(i)657 528 y Fk(2)696 503 y Fv(a)733 513 y Fl(i)755 528 y Fk(2)790 513 y Fl(i)812 528 y Fk(3)851 503 y Fv(:::)o(a)947 513 y Fl(i)969 528 y(t)p Fg(\000)p Fk(1)1076 513 y Fl(i)1098 526 y(t)1130 503 y Fv(a)1167 513 y Fl(i)1189 526 y(t)1218 513 y(i)1240 528 y Fk(1)537 594 y Fv(i)561 603 y Fk(1)596 594 y Fv(i)620 603 y Fk(1)1311 569 y Fy(=)27 b Fw(q)1461 503 y Fv(a)1498 513 y Fl(i)1520 528 y Fk(2)1555 513 y Fl(i)1577 528 y Fk(1)1616 503 y Fv(a)1653 513 y Fl(i)1675 528 y Fk(2)1711 513 y Fl(i)1733 528 y Fk(3)1771 503 y Fv(:::)o(a)1867 513 y Fl(i)1889 528 y(t)p Fg(\000)p Fk(1)1996 513 y Fl(i)2018 526 y(t)2051 503 y Fv(a)2088 513 y Fl(i)2110 526 y(t)2138 513 y(i)2160 528 y Fk(1)1457 594 y Fv(i)1481 603 y Fk(2)1516 594 y Fv(i)1540 603 y Fk(2)2231 569 y Fy(=)g Fx(\001)17 b(\001)g(\001)26 b Fy(=)i Fw(q)2629 503 y Fv(a)2666 513 y Fl(i)2688 528 y Fk(2)2723 513 y Fl(i)2745 528 y Fk(1)2784 503 y Fv(a)2821 513 y Fl(i)2843 528 y Fk(3)2878 513 y Fl(i)2900 528 y Fk(2)2939 503 y Fv(:::)o(a)3035 513 y Fl(i)3057 526 y(t)3086 513 y(i)3108 528 y(t)p Fg(\000)p Fk(1)3218 503 y Fv(a)3255 513 y Fl(i)3277 528 y Fk(1)3312 513 y Fl(i)3334 526 y(t)2625 594 y Fv(i)2649 603 y Fk(1)2684 594 y Fv(i)2708 603 y Fk(1)3371 569 y Fw(;)-180 795 y Fy(b)m(y)35 b(substituting)e Fw(q)548 736 y Fv(a)585 746 y Fl(i)607 761 y Fk(1)642 746 y Fl(i)664 761 y Fk(2)544 821 y Fv(i)568 830 y Fk(1)603 821 y Fv(i)627 830 y Fk(1)737 795 y Fy(=)d Fw(q)890 736 y Fv(a)927 746 y Fl(i)949 761 y Fk(2)984 746 y Fl(i)1006 761 y Fk(1)886 821 y Fv(i)910 830 y Fk(2)944 821 y Fv(i)968 830 y Fk(2)1049 795 y Fy(,)k(then)g Fw(q)1380 736 y Fv(a)1417 746 y Fl(i)1439 761 y Fk(2)1474 746 y Fl(i)1496 761 y Fk(1)1376 821 y Fv(i)1400 830 y Fk(2)1435 821 y Fv(i)1459 830 y Fk(2)1569 795 y Fy(=)c Fw(q)1722 736 y Fv(a)1759 746 y Fl(i)1781 761 y Fk(3)1816 746 y Fl(i)1838 761 y Fk(2)1718 821 y Fv(i)1742 830 y Fk(3)1777 821 y Fv(i)1801 830 y Fk(3)1915 795 y Fy(and)k(so)g(on.)47 b(The)35 b(claim)c(follo)m(ws)i(b)s(ecause)i Fw(q)3594 810 y Fv(i)3618 819 y Fk(1)3653 810 y Fv(i)3677 819 y Fk(1)3749 795 y Fy(is)f(not)f(a)-180 935 y(ro)s(ot)f(of)g(one.) 3681 b Fi(\003)-80 1158 y Fy(The)38 b(follo)m(wing)c(result)j(is)g(due) h(to)f(Rosso,)h(who)g(sk)m(etc)m(hed)i(an)d(argumen)m(t)g(in)f([Ro,)i (Th.)58 b(2.1].)f(W)-8 b(e)38 b(include)e(a)-180 1274 y(pro)s(of)c(for)g(completeness.)-180 1457 y FC(Lemma)k(2.5.)42 b Fy([Ro])p Fs(.)i(L)-5 b(et)35 b Fo(|)13 b Fy(=)27 b Fo(C)20 b Fs(.)51 b(Assume)34 b(that)h(the)f(br)-5 b(aiding)34 b(with)g(matrix)g Fy(\()p Fw(q)2884 1472 y Fv(ij)2945 1457 y Fy(\))g Fs(is)g(p)-5 b(ositive)34 b(and)f(of)h(Cartan)-180 1596 y(typ)-5 b(e)37 b(with)f(gener)-5 b(alize)g(d)36 b(Cartan)g(matrix)g Fy(\()p Fw(a)1473 1611 y Fv(ij)1534 1596 y Fy(\))p Fs(.)50 b(Then)36 b Fy(\()p Fw(a)1997 1611 y Fv(ij)2057 1596 y Fy(\))h Fs(is)f(symmetrizable,)g(with)h (symmetrizing)e(diagonal)-180 1736 y(matrix)d Fy(\()p Fw(d)219 1751 y Fv(i)247 1736 y Fy(\))p Fs(;)h(and)f(ther)-5 b(e)33 b(is)f(a)g(c)-5 b(ol)5 b(le)-5 b(ction)32 b(of)g(p)-5 b(ositive)32 b(numb)-5 b(ers)32 b Fy(\()p Fw(q)2316 1751 y Fv(I)2356 1736 y Fy(\))2394 1751 y Fv(I)5 b Fu(2X)2574 1736 y Fs(such)32 b(that)h Fy(\()p Fw(q)3071 1751 y Fv(ij)3132 1736 y Fy(\))f Fs(is)h(twist-e)-5 b(quivalent)32 b(to)-180 1875 y Fy(\()t Fn(b)-59 b Fw(q)-99 1890 y Fv(ij)-38 1875 y Fy(\))p Fs(,)34 b(wher)-5 b(e)1403 2061 y Fn(b)-59 b Fw(q)1442 2076 y Fv(ij)1531 2061 y Fy(=)27 b Fw(q)1681 2007 y Fv(d)1717 2017 y Fl(i)1744 2007 y Fv(a)1781 2017 y Fl(ij)1677 2088 y Fv(I)1875 2061 y Fs(for)35 b(al)5 b(l)34 b Fw(i;)17 b(j)34 b Fx(2)28 b Fw(I)8 b(:)-180 2267 y Fs(That)35 b(is,)f(the)h(br)-5 b(aiding)34 b(asso)-5 b(ciate)g(d)34 b(to)h Fy(\()t Fn(b)-59 b Fw(q)1382 2282 y Fv(ij)1442 2267 y Fy(\))35 b Fs(is)g(of)f(DJ-typ)-5 b(e.)-180 2513 y(Pr)g(o)g(of.)41 b Fy(W)-8 b(e)29 b(can)f(assume)g (that)g(the)g(braiding)f(is)g(indecomp)s(osable;)h(write)g Fw(I)36 b Fy(=)27 b Fx(f)p Fy(1)p Fw(;)17 b(:)g(:)g(:)f(;)h(\022)s Fx(g)p Fy(.)41 b(By)29 b(Remark)e(2.3,)i(w)m(e)-180 2653 y(can)35 b(assume)h(that)f Fw(q)598 2668 y Fv(ij)691 2653 y Fy(=)d Fw(q)842 2668 y Fv(j)t(i)902 2653 y Fy(,)k(for)f(all)e Fw(i;)17 b(j)38 b Fx(2)32 b Fw(I)8 b Fy(.)51 b(Giv)m(en)35 b Fw(j)j Fx(2)33 b Fw(I)8 b Fy(,)35 b(there)h(exists)g(a)f(sequence)j Fw(i)3260 2668 y Ft(1)3332 2653 y Fy(=)31 b(1)p Fw(;)17 b(i)3565 2668 y Ft(2)3605 2653 y Fw(;)g(:)g(:)g(:)e(;)i(i)3856 2668 y Fv(t)3918 2653 y Fy(=)32 b Fw(j)-180 2792 y Fy(of)g(elemen)m(ts) h(in)f Fw(I)8 b Fy(,)32 b(suc)m(h)i(that)f Fw(a)1037 2807 y Fv(i)1061 2819 y Fl(`)1091 2807 y Fv(i)1115 2819 y Fl(`)p Fk(+1)1254 2792 y Fx(6)p Fy(=)27 b(0)33 b(for)f(all)e Fw(`)p Fy(,)j(1)27 b Fx(\024)h Fw(`)g(<)f(t)p Fy(.)44 b(Then)1226 3019 y Fw(q)1273 2952 y Fv(a)1310 2962 y Fl(i)1332 2977 y Fk(1)1367 2962 y Fl(i)1389 2977 y Fk(2)1428 2952 y Fv(a)1465 2962 y Fl(i)1487 2977 y Fk(2)1523 2962 y Fl(i)1545 2977 y Fk(3)1584 2952 y Fv(:::)n(a)1679 2962 y Fl(i)1701 2977 y(t)p Fg(\000)p Fk(1)1808 2962 y Fl(i)1830 2975 y(t)1269 3043 y Ft(11)1894 3019 y Fy(=)28 b Fw(q)2045 2952 y Fv(a)2082 2962 y Fl(i)2104 2977 y Fk(2)2139 2962 y Fl(i)2161 2977 y Fk(1)2200 2952 y Fv(a)2237 2962 y Fl(i)2259 2977 y Fk(3)2294 2962 y Fl(i)2316 2977 y Fk(2)2355 2952 y Fv(:::)o(a)2451 2962 y Fl(i)2473 2975 y(t)2502 2962 y(i)2524 2977 y(t)p Fg(\000)p Fk(1)2041 3044 y Fv(j)t(j)2638 3019 y Fw(;)-180 3245 y Fy(as)38 b(in)e(the)i(pro)s(of)f(of)g(the)h (previous)g(Lemma.)57 b(Since)37 b Fw(\013)1900 3260 y Fv(j)1973 3245 y Fy(:=)f Fw(a)2163 3260 y Fv(i)2187 3269 y Fk(1)2222 3260 y Fv(i)2246 3269 y Fk(2)2285 3245 y Fw(a)2336 3260 y Fv(i)2360 3269 y Fk(2)2395 3260 y Fv(i)2419 3269 y Fk(3)2474 3245 y Fw(:)17 b(:)g(:)f(a)2656 3260 y Fv(i)2680 3269 y Fl(t)p Fg(\000)p Fk(1)2787 3260 y Fv(i)2811 3268 y Fl(t)2880 3245 y Fy(and)38 b Fw(\014)3130 3260 y Fv(j)3202 3245 y Fy(:=)e Fw(a)3392 3260 y Fv(i)3416 3269 y Fk(2)3451 3260 y Fv(i)3475 3269 y Fk(1)3514 3245 y Fw(a)3565 3260 y Fv(i)3589 3269 y Fk(3)3624 3260 y Fv(i)3648 3269 y Fk(2)3703 3245 y Fw(:)17 b(:)g(:)f(a)3885 3260 y Fv(i)3909 3268 y Fl(t)3937 3260 y Fv(i)3961 3269 y Fl(t)p Fg(\000)p Fk(1)-180 3384 y Fy(are)37 b(in)m(tegers)g(of)f(the) i(same)e(sign,)i(w)m(e)g(can)f(\014nd)g Fw(b)f Fx(2)f Fo(N)52 b Fy(and)37 b(a)f(family)f(\()p Fw(d)2610 3399 y Fv(i)2637 3384 y Fy(\))2675 3399 y Fv(i)p Fu(2)p Fv(I)2823 3384 y Fy(of)h(p)s(ositiv)m(e)h(in)m(tegers)g(suc)m(h)h(that)-170 3492 y Fw(\013)-108 3507 y Fv(j)p -170 3536 99 4 v -167 3628 a Fw(\014)-112 3643 y Fv(j)-32 3559 y Fy(=)84 3492 y Fw(d)135 3507 y Fv(j)p 84 3536 88 4 v 107 3628 a Fw(b)181 3559 y Fy(.)47 b(Let)34 b Fw(q)474 3574 y Fv(I)548 3559 y Fy(b)s(e)g(the)g(unique)g(p)s(ositiv)m(e)f(n)m(um)m(b)s(er)h(suc)m(h) i(that)d Fw(q)2368 3523 y Fv(b)2364 3584 y(I)2434 3559 y Fy(=)d Fw(q)2583 3574 y Ft(11)2658 3559 y Fy(.)47 b(Then)35 b Fw(q)3035 3505 y Fv(\014)3075 3515 y Fl(j)3031 3585 y Fv(j)t(j)3140 3559 y Fy(=)30 b Fw(q)3293 3505 y Fv(\013)3338 3515 y Fl(j)3289 3584 y Ft(11)3405 3559 y Fy(=)f Fw(q)3557 3499 y Fv(\014)3597 3509 y Fl(j)3639 3452 y(d)3671 3468 y(j)p 3639 3484 65 3 v 3658 3525 a(b)3553 3584 y Ft(11)3747 3559 y Fy(=)h Fw(q)3900 3505 y Fv(d)3936 3515 y Fl(j)3969 3505 y Fv(\014)4009 3515 y Fl(j)3896 3586 y Fv(I)4045 3559 y Fy(.)-180 3764 y(Th)m(us)k Fw(q)110 3779 y Fv(j)t(j)207 3764 y Fy(=)27 b Fw(q)357 3710 y Fv(d)393 3720 y Fl(j)353 3791 y Fv(I)430 3764 y Fy(;)33 b(and)g(for)f(all)e Fw(i;)17 b(j)34 b Fx(2)28 b Fw(I)8 b Fy(,)32 b Fw(q)1362 3779 y Fv(ij)1423 3764 y Fw(q)1466 3779 y Fv(j)t(i)1555 3764 y Fy(=)27 b Fw(q)1705 3710 y Fv(d)1741 3720 y Fl(i)1768 3710 y Fv(a)1805 3720 y Fl(ij)1701 3791 y Fv(I)1892 3764 y Fy(=)g Fw(q)2042 3710 y Fv(d)2078 3720 y Fl(j)2111 3710 y Fv(a)2148 3720 y Fl(j)s(i)2038 3791 y Fv(I)2207 3764 y Fy(,)33 b(and)f(the)h(claim)e(follo)m(ws.)793 b Fi(\003)-180 4010 y FC(Remark)37 b(2.6.)42 b Fy(The)33 b(diagonal)d(braiding)h(with)h(matrix)1663 4129 y Fn( )1789 4232 y Fw(q)134 b(q)2013 4196 y Fu(\000)p Ft(1)1741 4372 y Fw(q)1788 4336 y Fu(\000)p Ft(1)1974 4372 y Fx(\000)p Fw(q)2107 4129 y Fn(!)2202 4299 y Fw(;)-180 4588 y Fy(where)34 b Fw(q)i Fy(is)c(not)h(a)f(ro)s(ot)g(of)g(one,)h(is)f(generic)g(of)g (Cartan)h(t)m(yp)s(e)g(but)g(not)g(of)f(DJ-t)m(yp)s(e.)-80 4878 y(W)-8 b(e)30 b(no)m(w)g(state)h(a)e(v)m(ery)i(elegan)m(t)f (description)f(of)h(Nic)m(hols)f(algebras)g(used)i(b)m(y)g(Lusztig)e (in)g(a)h(fundamen)m(tal)f(w)m(a)m(y)-180 4994 y([L2].)-180 5177 y FC(Prop)s(osition)45 b(2.7.)h Fs(L)-5 b(et)43 b Fy(\()p Fw(V)5 b(;)17 b(c)p Fy(\))43 b Fs(b)-5 b(e)42 b(as)g(ab)-5 b(ove)42 b(and)g(assume)g(that)h Fw(q)2425 5192 y Fv(ij)2528 5177 y Fy(=)f Fw(q)2689 5192 y Fv(j)t(i)2792 5177 y Fs(for)g(al)5 b(l)43 b Fw(i;)17 b(j)6 b Fs(.)68 b(L)-5 b(et)42 b Fw(B)3573 5192 y Ft(1)3613 5177 y Fw(;)17 b(:)g(:)g(:)f(;)h(B)3906 5192 y Fv(\022)3987 5177 y Fs(b)-5 b(e)-180 5317 y(non-zer)g(o)33 b(elements)h(in)g Fo(|)-8 b Fs(.)38 b(Ther)-5 b(e)34 b(is)g(a)h(unique)f(biline)-5 b(ar)34 b(form)g Fy(\()17 b Fx(j)g Fy(\))26 b(:)i Fw(T)14 b Fy(\()p Fw(V)21 b Fy(\))h Fx(\002)g Fw(T)14 b Fy(\()p Fw(V)21 b Fy(\))27 b Fx(!)h Fo(|)20 b Fs(such)34 b(that)h Fy(\(1)p Fx(j)p Fy(1\))27 b(=)g(1)p eop %%Page: 7 7 7 6 bop 1010 0 a Fp(A)33 b(CHARA)n(CTERIZA)-6 b(TION)31 b(OF)i(QUANTUM)f(GR)n(OUPS)1151 b(7)-180 203 y Fs(and)70 396 y Fy(\()p Fw(x)163 411 y Fv(j)200 396 y Fx(j)p Fw(x)283 411 y Fv(j)320 396 y Fy(\))27 b(=)h Fw(\016)532 411 y Fv(ij)593 396 y Fw(B)667 411 y Fv(i)695 396 y Fw(;)216 b Fs(for)35 b(al)5 b(l)34 b Fw(i;)17 b(j)6 b Fy(;)-1563 b(\(2.5\))70 565 y(\()p Fw(x)p Fx(j)p Fw(y)t(y)295 524 y Fu(0)317 565 y Fy(\))28 b(=)f(\()p Fw(x)579 580 y Ft(\(1\))674 565 y Fx(j)p Fw(y)t Fy(\)\()p Fw(x)885 580 y Ft(\(2\))978 565 y Fx(j)p Fw(y)1058 524 y Fu(0)1080 565 y Fy(\))p Fw(;)216 b Fs(for)35 b(al)5 b(l)34 b Fw(x;)17 b(y)t(;)g(y)1903 524 y Fu(0)1952 565 y Fx(2)29 b Fw(T)14 b Fy(\()p Fw(V)21 b Fy(\);)-2479 b(\(2.6\))70 733 y(\()p Fw(xx)218 692 y Fu(0)242 733 y Fx(j)p Fw(y)t Fy(\))27 b(=)g(\()p Fw(x)p Fx(j)p Fw(y)659 749 y Ft(\(1\))753 733 y Fy(\)\()p Fw(x)884 692 y Fu(0)908 733 y Fx(j)p Fw(y)984 749 y Ft(\(2\))1077 733 y Fy(\))p Fw(;)216 b Fs(for)35 b(al)5 b(l)35 b Fw(x;)17 b(x)1808 692 y Fu(0)1831 733 y Fw(;)g(y)31 b Fx(2)d Fw(T)14 b Fy(\()p Fw(V)21 b Fy(\))p Fw(:)-2480 b Fy(\(2.7\))-180 927 y Fs(This)34 b(form)h(is)f(symmetric)h(and)f(also)g(satis\014es) -180 1120 y Fy(\(2.8\))751 b(\()p Fw(x)p Fx(j)p Fw(y)t Fy(\))27 b(=)g(0)p Fw(;)216 b Fs(for)35 b(al)5 b(l)34 b Fw(x)28 b Fx(2)g Fw(T)14 b Fy(\()p Fw(V)21 b Fy(\))2102 1135 y Fv(g)2142 1120 y Fw(;)c(y)31 b Fx(2)d Fw(T)14 b Fy(\()p Fw(V)21 b Fy(\))2584 1135 y Fv(h)2629 1120 y Fw(;)c(g)31 b Fx(6)p Fy(=)c Fw(h)h Fx(2)g Fy(\000)p Fw(:)-180 1313 y Fs(The)38 b(homo)-5 b(gene)g(ous)38 b(c)-5 b(omp)g(onents)38 b(of)h Fw(T)14 b Fy(\()p Fw(V)21 b Fy(\))39 b Fs(with)g(r)-5 b(esp)g(e)g(ct)39 b(to)g(its)g(usual)h Fo(N)8 b Fs(-gr)-5 b(ading)45 b(ar)-5 b(e)38 b(also)h(ortho)-5 b(gonal)38 b(with)-180 1453 y(r)-5 b(esp)g(e)g(ct)35 b(to)g Fy(\()17 b Fx(j)g Fy(\))p Fs(.)-80 1592 y(The)39 b(quotient)h Fw(T)14 b Fy(\()p Fw(V)21 b Fy(\))p Fw(=I)8 b Fy(\()p Fw(V)21 b Fy(\))p Fs(,)41 b(wher)-5 b(e)39 b Fw(I)8 b Fy(\()p Fw(V)21 b Fy(\))37 b(=)f Fx(f)p Fw(x)h Fx(2)g Fw(T)14 b Fy(\()p Fw(V)22 b Fy(\))36 b(:)h(\()p Fw(x)p Fx(j)p Fw(y)t Fy(\))f(=)h(0)p Fx(8)p Fw(y)i Fx(2)f Fw(T)14 b Fy(\()p Fw(V)21 b Fy(\))p Fx(g)39 b Fs(is)h(the)g(r)-5 b(adic)g(al)38 b(of)i(the)-180 1732 y(form,)45 b(is)e(c)-5 b(anonic)g(al)5 b(ly)42 b(isomorphic)g(to)h(the)g(Nichols)g(algebr)-5 b(a)42 b(of)h Fw(V)22 b Fs(.)70 b(Thus,)45 b Fy(\()17 b Fx(j)g Fy(\))42 b Fs(induc)-5 b(es)43 b(a)g(non-de)-5 b(gener)g(ate)-180 1871 y(biline)g(ar)34 b(form)g(on)h Fj(B)p Fy(\()p Fw(V)21 b Fy(\))p Fs(,)35 b(which)f(wil)5 b(l)34 b(b)-5 b(e)35 b(again)f(b)-5 b(e)34 b(denote)-5 b(d)35 b(by)g Fy(\()17 b Fx(j)g Fy(\))p Fs(.)-180 2077 y(Pr)-5 b(o)g(of.)41 b Fy(The)30 b(existence)g(and)f(uniqueness)i(of)d (the)h(form,)g(and)g(the)g(claims)e(ab)s(out)h(symmetry)h(and)g (orthogonalit)m(y)-8 b(,)-180 2216 y(are)36 b(pro)m(v)m(ed)i(exactly)f (as)g(in)e([L2,)j(1.2.3].)54 b(It)37 b(follo)m(ws)e(from)g(the)i(prop)s (erties)f(of)g(the)h(form)e(that)h Fw(I)8 b Fy(\()p Fw(V)22 b Fy(\))36 b(is)g(a)g(Hopf)-180 2356 y(ideal.)65 b(W)-8 b(e)40 b(no)m(w)h(c)m(hec)m(k)i(that)d Fw(T)14 b Fy(\()p Fw(V)21 b Fy(\))p Fw(=I)8 b Fy(\()p Fw(V)21 b Fy(\))40 b(is)g(the)h(Nic)m(hols)e(algebra)g(of)h Fw(V)21 b Fy(;)44 b(it)c(is)f(enough)i(to)f(v)m(erify)g(that)g(the)-180 2495 y(primitiv)m(e)24 b(elemen)m(ts)j(of)g Fw(T)14 b Fy(\()p Fw(V)21 b Fy(\))p Fw(=I)8 b Fy(\()p Fw(V)21 b Fy(\))26 b(are)h(in)f Fw(V)21 b Fy(.)42 b(Let)27 b Fw(x)g Fy(b)s(e)g(a)f(primitiv)m(e)e(elemen)m(t)j(in)f Fw(T)14 b Fy(\()p Fw(V)21 b Fy(\))p Fw(=I)8 b Fy(\()p Fw(V)21 b Fy(\),)28 b(homogeneous)-180 2635 y(of)33 b(degree)h Fw(n)29 b Fx(\025)g Fy(2.)45 b(Then)34 b(\()p Fw(x)p Fx(j)p Fw(y)t(y)1030 2599 y Fu(0)1052 2635 y Fy(\))28 b(=)h(0)k(for)g(all)e Fw(y)t Fy(,)h Fw(y)1754 2599 y Fu(0)1810 2635 y Fy(homogeneous)h(of)g(degrees)h Fw(m;)17 b(m)3075 2599 y Fu(0)3128 2635 y Fx(\025)29 b Fy(1)k(with)f Fw(m)23 b Fy(+)g Fw(m)3830 2599 y Fu(0)3882 2635 y Fy(=)29 b Fw(n)p Fy(;)-180 2774 y(th)m(us)34 b Fw(x)28 b Fy(=)f(0.)3697 b Fi(\003)-180 2975 y FC(Nic)m(hols)27 b(algebras)j(arising)e(from)g (quan)m(tum)i(groups.)49 b Fy(Let)26 b(\()p Fw(a)2376 2990 y Fv(ij)2437 2975 y Fy(\))2475 2990 y Ft(1)p Fu(\024)p Fv(i;j)t Fu(\024)p Fv(\022)2760 2975 y Fy(b)s(e)f(a)h(generalized)e (symmetrizable)-180 3091 y(Cartan)36 b(matrix)e([K];)k(let)d(\()p Fw(d)902 3106 y Ft(1)941 3091 y Fw(;)17 b(:)g(:)g(:)f(;)h(d)1211 3106 y Fv(\022)1249 3091 y Fy(\))36 b(b)s(e)g(p)s(ositiv)m(e)f(in)m (tegers)h(suc)m(h)i(that)d Fw(d)2676 3106 y Fv(i)2704 3091 y Fw(a)2755 3106 y Fv(ij)2849 3091 y Fy(=)e Fw(d)3009 3106 y Fv(j)3046 3091 y Fw(a)3097 3106 y Fv(j)t(i)3157 3091 y Fy(.)54 b(Let)36 b Fw(q)h Fx(2)c Fo(|)-8 b Fy(,)30 b Fw(q)37 b Fx(6)p Fy(=)d(0)p Fw(;)17 b Fy(1,)-180 3209 y(and)26 b(not)g(a)g(ro)s(ot)f(of)h(1.)41 b(W)-8 b(e)26 b(assume)h(that)f(the)g(braided)g(v)m(ector)h(space)g(\()p Fw(V)5 b(;)17 b(c)p Fy(\))26 b(is)g(giv)m(en)g(b)m(y)h(the)f(matrix)f Fw(q)3647 3224 y Fv(ij)3735 3209 y Fy(=)j Fw(q)3886 3173 y Fv(d)3922 3183 y Fl(i)3949 3173 y Fv(a)3986 3183 y Fl(ij)4045 3209 y Fy(.)-80 3380 y(W)-8 b(e)36 b(no)m(w)h(w)m(an)m(t)f (to)g(deriv)m(e)g(some)g(precise)h(information)c(ab)s(out)i(the)h (algebra)f Fj(B)p Fy(\()p Fw(V)22 b Fy(\))36 b(mainly)d(from)i([L2].)54 b(W)-8 b(e)-180 3496 y(need)34 b(to)e(consider)h(v)m(ector)g(spaces)i (o)m(v)m(er)e(the)g(\014eld)g(of)f(rational)e(functions)i Fo(Q)12 b Fy(\()p Fw(v)t Fy(\))5 b(.)-80 3720 y(Let)26 b(\()p Fw(W)m(;)17 b(d)p Fy(\))26 b(denote)h(a)f(\014nite-dimensional)d (braided)j(v)m(ector)h(space)g(o)m(v)m(er)h Fo(Q)11 b Fy(\()p Fw(v)t Fy(\))6 b(;)28 b(w)m(e)f(assume)g(that)f(the)h(braiding) -180 3836 y Fw(d)j Fy(is)f(diagonal)f(with)i(matrix)f(\()p Fw(v)1008 3800 y Fv(d)1044 3810 y Fl(i)1070 3800 y Fv(a)1107 3810 y Fl(ij)1166 3836 y Fy(\),)i(with)f(resp)s(ect)h(to)f(a)g(basis)g Fw(y)2294 3851 y Ft(1)2333 3836 y Fw(;)17 b(:)g(:)g(:)e(y)2555 3851 y Fv(\022)2594 3836 y Fy(.)43 b(W)-8 b(e)30 b(de\014ne)i(c)m (haracters)f Fw(\021)3618 3851 y Ft(1)3658 3836 y Fw(;)17 b(:)g(:)g(:)e(;)i(\021)3924 3851 y Fv(\022)3993 3836 y Fy(of)-180 3952 y(\000)32 b(b)m(y)1282 4082 y Fw(\021)1330 4097 y Fv(i)1358 4082 y Fy(\()p Fw(g)1443 4097 y Fv(j)1480 4082 y Fy(\))27 b(=)h Fw(v)1700 4040 y Fv(d)1736 4050 y Fl(i)1762 4040 y Fv(a)1799 4050 y Fl(ij)1858 4082 y Fw(;)212 b Fy(1)28 b Fx(\024)g Fw(i;)17 b(j)33 b Fx(\024)c Fw(\022)s(:)-180 4231 y Fy(W)-8 b(e)33 b(consider)g Fw(W)46 b Fy(as)33 b(a)f(Y)-8 b(etter-Drinfeld)31 b(mo)s(dule)g(o)m(v)m(er)j Fo(Q)11 b Fy(\()p Fw(v)t Fy(\))6 b(\000)32 b(b)m(y)i(de\014ning)e Fw(y)2788 4246 y Fv(i)2844 4231 y Fx(2)c Fw(W)3044 4195 y Fv(\021)3079 4205 y Fl(i)3030 4256 y Fv(g)3064 4266 y Fl(i)3109 4231 y Fy(,)33 b(for)f(all)e Fw(i)p Fy(.)-80 4486 y(Let)j Fw(v)142 4501 y Fv(i)200 4486 y Fy(:=)d Fw(v)384 4450 y Fv(d)420 4460 y Fl(i)450 4486 y Fy(,)k(1)c Fx(\024)g Fw(i)f Fx(\024)h Fw(\022)s Fy(.)47 b(W)-8 b(e)34 b(no)m(w)h(tak)m(e)f Fw(B)1648 4501 y Fv(i)1706 4486 y Fy(:=)1838 4405 y Fn(\000)1884 4486 y Fy(1)22 b Fx(\000)h Fw(v)2106 4445 y Fu(\000)p Ft(2)2102 4512 y Fv(i)2200 4405 y Fn(\001)2245 4428 y Fu(\000)p Ft(1)2369 4486 y Fx(2)30 b Fo(Q)12 b Fy(\()p Fw(v)t Fy(\))39 b(as)34 b(in)f([L2)o(,)h (1.2.3].)47 b(By)34 b(prop)s(osition)-180 4604 y(2.7,)c Fj(B)p Fy(\()p Fw(W)14 b Fy(\))29 b(is)g(Lusztig's)h(braided)f(Hopf)h (algebra)e FC(f)40 b Fy(\(with)29 b(Cartan)h(datum)f(giv)m(en)g(b)m(y)i Fw(i:j)j Fy(=)27 b Fw(d)3362 4619 y Fv(i)3390 4604 y Fw(a)3441 4619 y Fv(ij)3502 4604 y Fy(,)j(1)e Fx(\024)g Fw(i;)17 b(j)34 b Fx(\024)28 b Fw(\022)s Fy(.)-80 4897 y(Let)33 b Fx(A)27 b Fy(:=)h Fo(Q)11 b Fy([)q Fw(v)t(;)17 b(v)578 4860 y Fu(\000)p Ft(1)677 4897 y Fy(];)33 b(let)f([)p Fw(n)p Fy(])1017 4912 y Fv(i)1074 4897 y Fy(:=)1214 4829 y Fw(v)1265 4793 y Fv(n)1261 4854 y(i)1334 4829 y Fx(\000)23 b Fw(v)1485 4788 y Fu(\000)p Fv(n)1481 4855 y(i)p 1214 4874 373 4 v 1229 4970 a Fw(v)1276 4985 y Fv(i)1327 4970 y Fx(\000)f Fw(v)1477 4928 y Fu(\000)p Ft(1)1473 4995 y Fv(i)1596 4897 y Fy(,)33 b([)p Fw(r)s Fy(])1757 4912 y Fv(i)1785 4897 y Fy(!)28 b(=)g([1])2047 4912 y Fv(i)2075 4897 y Fy([2])2178 4912 y Fv(i)2223 4897 y Fw(:)17 b(:)g(:)f Fy([)p Fw(r)s Fy(])2455 4912 y Fv(i)2483 4897 y Fy(.)44 b(Let)33 b Fj(B)p Fy(\()p Fw(W)14 b Fy(\))2999 4912 y Fu(A)3092 4897 y Fy(b)s(e)33 b(the)g Fx(A)p Fy(-subalgebra)e(of)-180 5078 y Fj(B)p Fy(\()p Fw(W)14 b Fy(\))32 b(generated)h(b)m(y)h(all)1191 5257 y Fw(y)1243 5206 y Ft(\()p Fv(r)r Ft(\))1239 5282 y Fv(i)1363 5257 y Fy(:=)1537 5189 y Fw(y)1589 5153 y Fv(r)1585 5214 y(i)p 1503 5234 157 4 v 1503 5325 a Fy([)p Fw(r)s Fy(])1604 5340 y Fv(i)1632 5325 y Fy(!)1670 5257 y Fw(;)211 b Fy(1)28 b Fx(\024)g Fw(i)g Fx(\024)g Fw(\022)s(;)114 b(r)31 b Fx(\025)d Fy(0)p Fw(:)p eop %%Page: 8 8 8 7 bop -180 0 a Fp(8)884 b(NICOL)1001 -19 y(\023)991 0 y(AS)24 b(ANDR)n(USKIEWITSCH)f(AND)h(HANS-J)2419 -19 y(\177)2409 0 y(UR)n(GEN)f(SCHNEIDER)-80 203 y Fy(The)34 b(canonical)f(bilinear)e(form)i(\()17 b Fx(j)g Fy(\))28 b(:)i Fj(B)p Fy(\()p Fw(W)14 b Fy(\))22 b Fx(\002)i Fj(B)p Fy(\()p Fw(W)14 b Fy(\))29 b Fx(!)g Fo(Q)12 b Fy(\()p Fw(v)t Fy(\))39 b(do)s(es)34 b(not)g(restrict)g(to)f(an)h Fx(A)p Fy(-bilinear)c(form)-180 319 y Fj(B)p Fy(\()p Fw(W)14 b Fy(\))90 334 y Fu(A)172 319 y Fx(\002)23 b Fj(B)p Fy(\()p Fw(W)14 b Fy(\))542 334 y Fu(A)630 319 y Fx(!)27 b(A)p Fy(,)32 b(since)h(b)m(y)h([L2,)e(1.4.4],)1268 586 y(\()p Fw(y)1358 536 y Ft(\()p Fv(r)r Ft(\))1354 612 y Fv(i)1449 586 y Fx(j)p Fw(y)1529 536 y Ft(\()p Fv(r)r Ft(\))1525 612 y Fv(i)1621 586 y Fy(\))c(=)f Fw(v)1851 493 y Fl(r)r Fk(\()p Fl(r)r Fk(+1\))p 1851 511 186 3 v 1929 552 a(2)1837 612 y Fv(i)2061 432 y Fn(\000)2107 513 y Fw(v)2154 528 y Fv(i)2204 513 y Fx(\000)c Fw(v)2355 471 y Fu(\000)p Ft(1)2351 538 y Fv(i)2449 432 y Fn(\001)2495 454 y Fu(\000)p Fv(r)p 2061 564 527 4 v 2246 655 a Fy([)p Fw(r)s Fy(])2347 670 y Fv(i)2375 655 y Fy(!)2597 586 y Fw(:)-180 848 y Fy(F)-8 b(ollo)m(wing)30 b(an)i(idea)g(of)g(M)s(\177) -51 b(uller)31 b([Mu],)i(w)m(e)h(de\014ne)1721 822 y Fn(e)1705 848 y Fj(B)p Fy(\()p Fw(W)14 b Fy(\))1975 863 y Fu(A)2067 848 y Fy(as)33 b(the)g Fx(A)p Fy(-subalgebra)e(of)h Fj(B)p Fy(\()p Fw(W)14 b Fy(\))33 b(generated)g(b)m(y)g(all)1062 1027 y Fn(e)-59 b Fw(y)1106 1042 y Fv(i)1162 1027 y Fy(:=)1292 947 y Fn(\000)1338 1027 y Fy(1)22 b Fx(\000)g Fw(v)1559 986 y Fu(\000)p Ft(2)1555 1053 y Fv(i)1654 947 y Fn(\001)1716 1027 y Fw(y)1764 1042 y Fv(i)1819 1027 y Fy(=)28 b Fw(B)2002 986 y Fu(\000)p Ft(1)1997 1053 y Fv(i)2096 1027 y Fw(y)2144 1042 y Fv(i)2172 1027 y Fw(;)212 b Fy(1)27 b Fx(\024)h Fw(i)g Fx(\024)g Fw(\022)s(:)-80 1230 y Fy(Then)36 b(\()17 b Fx(j)g Fy(\))34 b(restricts)i(to)f(an)g Fx(A)p Fy(-bilinear)d(form)j (\()17 b Fx(j)g Fy(\))31 b(:)h Fj(B)p Fy(\()p Fw(W)14 b Fy(\))2186 1245 y Fu(A)2271 1230 y Fx(\002)2388 1204 y Fn(e)2372 1230 y Fj(B)p Fy(\()p Fw(W)g Fy(\))2642 1245 y Fu(A)2735 1230 y Fx(!)32 b(A)p Fy(,)j(b)m(y)i(the)f(argumen)m(t)f(in) f([Mu)q(,)-180 1346 y(Lemma)d(2.2)h(\(a\)].)-80 1477 y(Note)23 b(that)f Fj(B)p Fy(\()p Fw(W)14 b Fy(\))617 1492 y Fu(A)700 1477 y Fy(and)896 1451 y Fn(e)880 1477 y Fj(B)p Fy(\()p Fw(W)g Fy(\))1150 1492 y Fu(A)1233 1477 y Fy(inherit)22 b(the)h(Hopf)g(algebra)e(structure)j(from)e Fj(B)p Fy(\()p Fw(W)14 b Fy(\),)24 b(since)g Fx(A)e Fy(is)g(a)h (principal)-180 1594 y(ideal)31 b(domain)g(with)h(quotien)m(t)h (\014eld)f Fo(Q)12 b Fy(\()p Fw(v)t Fy(\))5 b(.)-80 1833 y(Let)28 b Fx(W)37 b Fy(b)s(e)29 b(the)g(W)-8 b(eyl)29 b(group)f(of)g(the)h(generalized)f(Cartan)g(matrix)f(\()p Fw(a)2532 1848 y Fv(ij)2593 1833 y Fy(\))h([L2,)h(2.1.1];)h(then)f Fx(W)37 b Fy(is)28 b(\014nite)g(if)g(and)-180 1950 y(only)36 b(if)g(\()p Fw(a)221 1965 y Fv(ij)282 1950 y Fy(\))g(is)g(of)h (\014nite)f(t)m(yp)s(e.)57 b(Let)37 b Fw(w)g Fx(2)e(W)46 b Fy(b)s(e)37 b(an)f(elemen)m(t)h(with)f(reduced)j(expression)f Fw(w)f Fy(=)e Fw(s)3601 1965 y Fv(i)3625 1974 y Fk(1)3663 1950 y Fw(s)3709 1965 y Fv(i)3733 1974 y Fk(2)3789 1950 y Fw(:)17 b(:)g(:)f(s)3966 1965 y Fv(i)3990 1976 y Fl(P)4045 1950 y Fy(,)-180 2067 y Fw(P)41 b Fx(2)28 b Fo(N)9 b Fy(.)50 b(F)-8 b(or)31 b(an)m(y)j Fw(c)27 b Fy(=)h(\()p Fw(c)773 2082 y Ft(1)812 2067 y Fw(;)17 b(:)g(:)g(:)f(;)h(c)1073 2082 y Fv(P)1131 2067 y Fy(\))28 b Fx(2)g Fo(N)1357 2031 y Fv(P)1422 2067 y Fy(,)k(let)894 2277 y Fw(L)p Fy(\()p Fw(c)p Fy(\))c(:=)g Fw(y)1289 2226 y Ft(\()p Fv(c)1347 2235 y Fk(1)1381 2226 y Ft(\))1285 2302 y Fv(i)1309 2311 y Fk(1)1429 2277 y Fw(T)1486 2292 y Fv(i)1510 2301 y Fk(1)1565 2166 y Fn(\020)1625 2277 y Fw(y)1677 2226 y Ft(\()p Fv(c)1735 2235 y Fk(2)1769 2226 y Ft(\))1673 2302 y Fv(i)1697 2311 y Fk(2)1800 2166 y Fn(\021)1876 2277 y Fw(:)17 b(:)g(:)f(T)2064 2292 y Fv(i)2088 2301 y Fk(1)2144 2277 y Fw(T)2201 2292 y Fv(i)2225 2301 y Fk(2)2281 2277 y Fw(:)h(:)g(:)f(T)2469 2292 y Fv(i)2493 2303 y Fl(P)8 b Fg(\000)p Fk(1)2643 2166 y Fn(\020)2703 2277 y Fw(y)2755 2226 y Ft(\()p Fv(c)2813 2237 y Fl(P)2863 2226 y Ft(\))2751 2302 y Fv(i)2775 2313 y Fl(P)2894 2166 y Fn(\021)2970 2277 y Fw(;)-180 2486 y Fy(where)36 b Fw(T)161 2501 y Fv(i)185 2513 y Fl(`)253 2486 y Fy(are)f(the)g Fo(Q)11 b Fy(\()p Fw(v)t Fy(\))6 b(-algebra)33 b(automorphisms)g(of)h FC(U)g Fy(named)g Fw(T)2474 2450 y Fu(0)2460 2511 y Fv(i)2484 2523 y Fl(`)2515 2511 y Fv(;)p Fu(\000)p Ft(1)2663 2486 y Fy(in)g([L2,)h(37.1.3].)48 b(Note)35 b(that)f Fw(L)p Fy(\()p Fw(c)p Fy(\))d(=)-180 2607 y Fw(L)p Fy(\()p FC(h)p Fw(;)17 b(c;)g Fy(0)p Fw(;)g Fy(1\),)32 b(with)g FC(h)c Fy(:=)g(\()p Fw(i)869 2622 y Ft(1)908 2607 y Fw(;)17 b(:)g(:)g(:)f(;)h(i)1160 2622 y Fv(P)1219 2607 y Fy(\),)32 b(in)g([L2,)g(38.2.3].)43 b(By)33 b([L2,)g(41.1.3],)754 2816 y Fw(T)811 2831 y Fv(i)835 2840 y Fk(1)890 2816 y Fw(T)947 2831 y Fv(i)971 2840 y Fk(2)1027 2816 y Fw(:)17 b(:)g(:)f(T)1215 2831 y Fv(i)1239 2843 y Fl(`)p Fg(\000)p Fk(1)1368 2706 y Fn(\020)1428 2816 y Fw(y)1480 2765 y Ft(\()p Fv(r)r Ft(\))1476 2842 y Fv(i)1500 2854 y Fl(`)1572 2706 y Fn(\021)1659 2816 y Fx(2)28 b Fj(B)p Fy(\()p Fw(W)14 b Fy(\))2023 2831 y Fu(A)2083 2816 y Fw(;)212 b Fy(1)28 b Fx(\024)g Fw(`)f(<)h(P)s(;)114 b(r)30 b Fx(\025)e Fy(0)p Fw(;)-180 3032 y Fy(where)42 b(w)m(e)f(ha)m(v)m(e)h(iden)m(ti\014ed)f Fj(B)p Fy(\()p Fw(W)14 b Fy(\))40 b(with)g FC(U)1554 2996 y Ft(+)1653 3032 y Fy(b)m(y)i([L2,)g(3.2.6],)g(that)f(is)f(w)m(e)h (iden)m(tify)f Fw(E)3212 3047 y Fv(i)3282 3032 y Fy(:=)h Fw(\022)3474 2991 y Ft(+)3471 3058 y Fv(i)3574 3032 y Fy(in)f(Lusztig's)-180 3149 y(notation)31 b(with)h Fw(y)480 3164 y Fv(i)508 3149 y Fy(.)44 b(W)-8 b(e)33 b(denote)1078 3327 y Fw(z)1123 3342 y Fv(`)1184 3327 y Fy(:=)27 b Fw(T)1371 3342 y Fv(i)1395 3351 y Fk(1)1451 3327 y Fw(T)1508 3342 y Fv(i)1532 3351 y Fk(2)1588 3327 y Fw(:)17 b(:)g(:)f(T)1776 3342 y Fv(i)1800 3354 y Fl(`)p Fg(\000)p Fk(1)1929 3327 y Fy(\()p Fw(y)2015 3342 y Fv(i)2039 3354 y Fl(`)2073 3327 y Fy(\))g Fw(;)212 b Fy(1)27 b Fx(\024)i Fw(`)e Fx(\024)h Fw(P)s(:)-180 3505 y Fy(Then)34 b Fw(z)120 3520 y Fv(`)181 3505 y Fx(2)28 b Fj(B)p Fy(\()p Fw(W)14 b Fy(\))545 3520 y Fu(A)637 3505 y Fy(and)760 3714 y Fw(z)809 3673 y Fv(r)805 3739 y(`)875 3714 y Fy(=)28 b([)p Fw(r)s Fy(])1080 3729 y Fv(i)1104 3741 y Fl(`)1138 3714 y Fy(!)17 b Fw(T)1239 3729 y Fv(i)1263 3738 y Fk(1)1318 3714 y Fw(T)1375 3729 y Fv(i)1399 3738 y Fk(2)1455 3714 y Fw(:)g(:)g(:)f(T)1643 3729 y Fv(i)1667 3741 y Fl(`)p Fg(\000)p Fk(1)1796 3604 y Fn(\020)1856 3714 y Fw(y)1908 3664 y Ft(\()p Fv(r)r Ft(\))1904 3740 y Fv(i)1928 3752 y Fl(`)2000 3604 y Fn(\021)2076 3714 y Fw(;)211 b Fy(1)28 b Fx(\024)g Fw(`)g Fx(\024)g Fw(P)s(;)114 b(r)30 b Fx(\025)e Fy(0)p Fw(:)-180 3931 y FC(Theorem)37 b(2.8.)42 b Fs(\(Lusztig\).)j(F) -7 b(or)33 b(al)5 b(l)35 b Fw(c)28 b Fy(=)f(\()p Fw(c)1540 3946 y Ft(1)1580 3931 y Fw(;)17 b(:)g(:)g(:)e(;)i(c)1840 3946 y Fv(P)1899 3931 y Fy(\))p Fw(;)g(c)2023 3895 y Fu(0)2073 3931 y Fx(2)28 b Fo(N)2233 3895 y Fv(P)-180 4132 y Fy(\(2.9\))993 b(\()p Fw(L)p Fy(\()p Fw(c)p Fy(\))p Fx(j)p Fw(L)p Fy(\()p Fw(c)1410 4091 y Fu(0)1433 4132 y Fy(\)\))28 b(=)g Fw(\016)1684 4147 y Fv(c;c)1766 4128 y Fg(0)1860 4037 y Fn(Y)1808 4249 y Ft(1)p Fu(\024)p Fv(s)p Fu(\024)p Fv(P)2110 4037 y Fn(Y)2056 4248 y Ft(1)p Fu(\024)p Fv(t)p Fu(\024)p Fv(c)2257 4256 y Fl(s)2307 4051 y Fn(\000)2353 4132 y Fy(1)22 b Fx(\000)h Fw(v)2575 4091 y Fu(\000)p Ft(2)p Fv(t)2571 4158 y(i)2694 4051 y Fn(\001)2740 4074 y Fu(\000)p Ft(1)2851 4132 y Fw(:)-180 4429 y Fs(Pr)-5 b(o)g(of.)41 b Fy(This)33 b(follo)m(ws)e(from)g([L2,)i (38.2.3)f(and)g(1.4.4].)2180 b Fi(\003)-80 4668 y Fy(W)-8 b(e)33 b(regard)f Fo(|)18 b Fy(as)33 b(an)f Fx(A)p Fy(-algebra)f(via)h (the)h(algebra)e(map)h Fw(')27 b Fy(:)h Fx(A)f(!)h Fo(|)18 b Fy(giv)m(en)32 b(b)m(y)i Fw(')p Fy(\()p Fw(v)t Fy(\))27 b(=)g Fw(q)t Fy(.)44 b(W)-8 b(e)33 b(de\014ne)776 4861 y Fj(B)p Fy(\()p Fw(W)14 b Fy(\))1046 4876 y Fh(|)1115 4861 y Fy(:=)27 b Fj(B)p Fy(\()p Fw(W)14 b Fy(\))1515 4876 y Fu(A)1597 4861 y Fx(\012)1674 4876 y Fu(A)1758 4861 y Fo(|)-9 b Fw(;)2068 4835 y Fn(e)2052 4861 y Fj(B)p Fy(\()p Fw(W)14 b Fy(\))2322 4876 y Fh(|)2390 4861 y Fy(:=)2537 4835 y Fn(e)2521 4861 y Fj(B)p Fy(\()p Fw(W)g Fy(\))2791 4876 y Fu(A)2873 4861 y Fx(\012)2950 4876 y Fu(A)3033 4861 y Fo(|)-8 b Fw(:)-180 5054 y Fy(Then)38 b Fj(B)p Fy(\()p Fw(W)14 b Fy(\))349 5069 y Fh(|)390 5054 y Fy(,)471 5028 y Fn(e)455 5054 y Fj(B)p Fy(\()p Fw(W)g Fy(\))725 5069 y Fh(|)802 5054 y Fy(are)37 b(graded)g(braided)g (Hopf)g(algebras)f(in)2395 5018 y Fh(|)-14 b Ft(\000)2395 5080 y Fh(|)g Ft(\000)2481 5054 y Fx(Y)8 b(D)39 b Fy(and)e(b)m(y)h (tensoring)e(with)h Fo(|)22 b Fy(o)m(v)m(er)38 b Fx(A)p Fy(,)-180 5170 y(w)m(e)c(get)e(a)g(bilinear)f(form)1346 5317 y(\()17 b Fx(j)g Fy(\))27 b(:)g Fj(B)p Fy(\()p Fw(W)14 b Fy(\))1835 5332 y Fh(|)1898 5317 y Fx(\002)2014 5291 y Fn(e)1998 5317 y Fj(B)p Fy(\()p Fw(W)g Fy(\))2268 5332 y Fh(|)2336 5317 y Fx(!)27 b Fo(|)-8 b Fw(:)p eop %%Page: 9 9 9 8 bop 1010 0 a Fp(A)33 b(CHARA)n(CTERIZA)-6 b(TION)31 b(OF)i(QUANTUM)f(GR)n(OUPS)1151 b(9)-180 218 y Fy(De\014ne)36 b Fw(\031)g Fy(:)d Fw(T)14 b Fy(\()p Fw(V)21 b Fy(\))33 b Fx(!)f Fj(B)p Fy(\()p Fw(W)14 b Fy(\))936 233 y Fh(|)1012 218 y Fy(and)37 b Fn(e)-57 b Fw(\031)37 b Fy(:)c Fw(T)14 b Fy(\()p Fw(V)21 b Fy(\))32 b Fx(!)1762 192 y Fn(e)1745 218 y Fj(B)q Fy(\()p Fw(W)14 b Fy(\))2016 233 y Fh(|)2091 218 y Fy(b)m(y)37 b Fw(\031)t Fy(\()p Fw(x)2382 233 y Fv(i)2410 218 y Fy(\))c(:=)f Fw(y)2664 233 y Fv(i)2716 218 y Fx(\012)25 b Fy(1,)37 b Fn(e)-56 b Fw(\031)t Fy(\()p Fw(x)3082 233 y Fv(i)3110 218 y Fy(\))33 b(:=)i Fn(e)-58 b Fw(y)3364 233 y Fv(i)3416 218 y Fx(\012)25 b Fy(1,)35 b(1)e Fx(\024)g Fw(i)g Fx(\024)g Fw(\022)s Fy(.)-180 349 y(Since)c Fw(\031)j Fy(and)f Fn(e)-57 b Fw(\031)33 b Fy(induce)c(isomorphisms)e(of)h(braided)g(v)m(ector)i(spaces)h(of)d (\()p Fw(V)5 b(;)17 b(c)p Fy(\))28 b(with)h Fj(B)p Fy(\()p Fw(W)14 b Fy(\))3230 364 y Fh(|)3270 349 y Fy(\(1\))29 b(and)3626 323 y Fn(e)3610 349 y Fj(B)p Fy(\()p Fw(W)14 b Fy(\))3880 364 y Fh(|)3920 349 y Fy(\(1\),)-180 465 y(the)33 b(comp)s(osition)805 621 y(\()17 b Fx(j)g Fy(\))26 b(:)i Fw(T)14 b Fy(\()p Fw(V)21 b Fy(\))h Fx(\002)h Fw(T)14 b Fy(\()p Fw(V)21 b Fy(\))1699 564 y Fv(\031)r Fu(\002)r Fm(e)-41 b Fv(\031)1645 621 y Fx(\000)-30 b(\000)-22 b(\000)-30 b(!)48 b Fj(B)p Fy(\()p Fw(W)14 b Fy(\))2212 636 y Fh(|)2275 621 y Fx(\002)2391 595 y Fn(e)2375 621 y Fj(B)p Fy(\()p Fw(W)g Fy(\))2645 636 y Fh(|)2810 557 y Ft(\()e Fu(j)f Ft(\))2734 621 y Fx(\000)-30 b(\000)-21 b(\000)-30 b(!)48 b Fo(|)-180 753 y Fy(is)37 b(the)g(canonical)f (bilinear)f(form)h(of)h Fw(T)14 b Fy(\()p Fw(V)21 b Fy(\))37 b(as)g(in)g(Prop)s(osition)e(2.7)i(with)g(scalars)g Fw(B)3053 768 y Fv(i)3116 753 y Fy(=)f(1,)i(1)27 b Fx(\024)i Fw(i)f Fx(\024)g Fw(\022)s Fy(.)57 b(These)-180 869 y(argumen)m(ts)33 b(allo)m(w)e(to)h(adapt)g(man)m(y)h(results)g(of)f(Lusztig)g(to)h(the)g (case)g(when)h Fw(q)i Fy(is)c(not)h(a)f(ro)s(ot)g(of)g(1.)-180 1075 y FC(Theorem)39 b(2.9.)k Fy([Ro,)35 b(Theorem)g(15])p Fs(;)i Fy([L2)o(,)f(Section)e(37])p Fs(.)50 b(L)-5 b(et)37 b Fy(\()p Fw(V)5 b(;)17 b(c)p Fy(\))36 b Fs(b)-5 b(e)36 b(a)h(br)-5 b(aide)g(d)36 b(ve)-5 b(ctor)36 b(sp)-5 b(ac)g(e)36 b(of)g(DJ-typ)-5 b(e.)-180 1215 y(Then)34 b Fj(B)p Fy(\()p Fw(V)22 b Fy(\))27 b Fx(')h Fo(|)-8 b Fx(h)o Fw(x)604 1230 y Ft(1)638 1215 y Fw(;)17 b(:)g(:)g(:)f(;)h(x)912 1230 y Fv(\022)951 1215 y Fx(j)p Fy(ad)1098 1230 y Fv(c)1133 1215 y Fy(\()p Fw(x)1226 1230 y Fv(i)1254 1215 y Fy(\))1292 1179 y Ft(1)p Fu(\000)p Fv(a)1419 1189 y Fl(ij)1507 1215 y Fy(=)27 b(0)p Fw(;)17 b Fy(1)27 b Fx(\024)h Fw(i)g Fx(6)p Fy(=)g Fw(j)33 b Fx(\024)c Fw(\022)s Fx(i)p Fs(.)1649 b Fi(\003)-80 1353 y Fy(The)33 b(follo)m(wing)d(Theorem)j(is)f(part)g (of)g(the)h(folklore)e(of)h(quan)m(tum)h(groups.)-180 1515 y FC(Theorem)d(2.10.)38 b Fs(L)-5 b(et)30 b Fy(\()p Fw(V)5 b(;)17 b(c)p Fy(\))29 b Fs(b)-5 b(e)29 b(a)g(br)-5 b(aide)g(d)29 b(ve)-5 b(ctor)29 b(sp)-5 b(ac)g(e)29 b(of)g(DJ-typ)-5 b(e,)31 b(with)e(gener)-5 b(alize)g(d)28 b(Cartan)h(matrix)g Fy(\()p Fw(a)3943 1530 y Fv(ij)4004 1515 y Fy(\))p Fs(.)-80 1654 y(\(i\).)44 b(If)34 b(the)h(Gelfand-Kiril)5 b(lov)34 b(dimension)f(of)h Fj(B)p Fy(\()p Fw(V)22 b Fy(\))35 b Fs(is)f(\014nite,)h(then)f Fy(\()p Fw(a)2644 1669 y Fv(ij)2705 1654 y Fy(\))h Fs(is)g(a)f(\014nite)h(Cartan)f(matrix.)-80 1794 y(\(ii\).)48 b(If)35 b Fy(\()p Fw(a)330 1809 y Fv(ij)391 1794 y Fy(\))h Fs(is)g(a)g(\014nite)g(Cartan)g(matrix,)g(then)g(the)g (Gelfand-Kiril)5 b(lov)35 b(dimension)f(of)i Fj(B)p Fy(\()p Fw(V)22 b Fy(\))36 b Fs(is)g(\014nite)g(and)-180 1933 y(e)-5 b(qual)35 b(to)g(the)g(numb)-5 b(er)34 b(of)h(p)-5 b(ositive)34 b(r)-5 b(o)g(ots.)-180 2127 y(Pr)g(o)g(of.)41 b Fy(\(i\).)49 b(W)-8 b(e)36 b(can)f(assume)g(that)g(the)g(braiding)e (is)i(connected.)52 b(Let)35 b Fw(w)f Fx(2)e(W)43 b Fy(b)s(e)35 b(an)g(elemen)m(t)g(with)f(reduced)-180 2267 y(expression)d Fw(w)f Fy(=)e Fw(s)537 2282 y Fv(i)561 2291 y Fk(1)599 2267 y Fw(s)645 2282 y Fv(i)669 2291 y Fk(2)725 2267 y Fw(:)17 b(:)g(:)f(s)902 2282 y Fv(i)926 2293 y Fl(P)981 2267 y Fy(,)31 b Fw(P)41 b Fx(2)28 b Fo(N)9 b Fy(.)48 b(W)-8 b(e)30 b(k)m(eep)i(the)e(notation)f(ab)s(o)m(v)m(e.)43 b(F)-8 b(or)29 b(all)f Fw(`)p Fy(,)i(1)e Fx(\024)g Fw(`)f Fx(\024)i Fw(P)14 b Fy(,)29 b(w)m(e)i(c)m(ho)s(ose)g(an)-180 2406 y(elemen)m(t)j Fw(t)217 2421 y Fv(`)281 2406 y Fx(2)d Fw(T)14 b Fy(\()p Fw(V)21 b Fy(\))34 b(with)g Fw(\031)t Fy(\()p Fw(t)993 2421 y Fv(`)1026 2406 y Fy(\))c(=)g Fw(z)1245 2421 y Fv(`)1302 2406 y Fx(\012)24 b Fy(1,)34 b(and)g(set)h Fw(b)1899 2421 y Fv(`)1963 2406 y Fy(:=)f(canonical)f (image)f(of)i Fw(t)2961 2421 y Fv(`)3029 2406 y Fy(in)f Fj(B)p Fy(\()p Fw(V)22 b Fy(\).)48 b(W)-8 b(e)34 b(claim)e(that)-180 2546 y(the)h(ordered)g(monomials)d Fw(b)870 2502 y Fv(c)901 2511 y Fk(1)870 2570 y Ft(1)939 2546 y Fw(b)980 2502 y Fv(c)1011 2511 y Fk(2)980 2570 y Ft(2)1067 2546 y Fw(:)17 b(:)g(:)f(b)1239 2500 y Fv(c)1270 2511 y Fl(P)1239 2573 y Fv(P)1325 2546 y Fy(,)33 b Fw(c)1427 2561 y Ft(1)1466 2546 y Fw(;)17 b(:)g(:)g(:)f(;)h(c)1727 2561 y Fv(P)1813 2546 y Fx(\025)28 b Fy(0,)33 b(are)f(linearly)f(indep)s(enden)m(t.)-80 2729 y(T)-8 b(o)33 b(pro)m(v)m(e)h(the)f(claim,)e(w)m(e)j(c)m(ho)s(ose) g Fw(a)1288 2744 y Fv(c)1351 2729 y Fx(2)28 b(A)33 b Fy(suc)m(h)h(that)f Fw(a)2041 2744 y Fv(c)2076 2729 y Fw(L)p Fy(\()p Fw(c)p Fy(\))28 b Fx(2)2399 2704 y Fn(e)2383 2729 y Fj(B)p Fy(\()p Fw(W)14 b Fy(\))2653 2744 y Fu(A)2746 2729 y Fy(for)32 b(all)f Fw(c)d Fy(=)g(\()p Fw(c)3285 2744 y Ft(1)3325 2729 y Fw(;)17 b(:)g(:)g(:)f(;)h(c)3586 2744 y Fv(P)3644 2729 y Fy(\))28 b Fx(2)h Fo(N)3871 2693 y Fv(P)3935 2729 y Fy(.)45 b(If)-172 2844 y Fn(e)-180 2869 y Fw(L)p Fy(\()p Fw(c)p Fy(\))28 b(:=)g Fw(a)214 2884 y Fv(c)248 2869 y Fw(L)p Fy(\()p Fw(c)p Fy(\))449 2794 y Fn(Q)543 2898 y Ft(1)p Fu(\024)p Fv(s)p Fu(\024)p Fv(P)796 2794 y Fn(Q)890 2898 y Ft(1)p Fu(\024)p Fv(t)p Fu(\024)p Fv(c)1091 2906 y Fl(s)1146 2788 y Fn(\000)1191 2869 y Fy(1)22 b Fx(\000)h Fw(v)1413 2828 y Fu(\000)p Ft(2)p Fv(t)1409 2895 y(i)1532 2788 y Fn(\001)1606 2869 y Fx(2)1716 2843 y Fn(e)1700 2869 y Fj(B)p Fy(\()p Fw(W)14 b Fy(\))1970 2884 y Fu(A)2030 2869 y Fy(,)33 b(then)-180 3059 y(\(2.10\))1431 b(\()p Fw(L)p Fy(\()p Fw(c)p Fy(\))p Fx(j)1759 3034 y Fn(e)1751 3059 y Fw(L)p Fy(\()p Fw(c)1897 3018 y Fu(0)1920 3059 y Fy(\)\))28 b(=)f Fw(\016)2170 3074 y Fv(c;c)2252 3055 y Fg(0)2278 3059 y Fw(a)2329 3074 y Fv(c)2364 3059 y Fw(;)-180 3243 y Fy(for)43 b(all)f Fw(c;)17 b(c)255 3207 y Fu(0)325 3243 y Fx(2)47 b Fo(N)504 3207 y Fv(P)569 3243 y Fy(,)f(b)m(y)g(\(2.9\).)77 b(It)44 b(follo)m(ws)f(that)g Fw(\031)t Fy(\()p Fw(t)1898 3200 y Fv(c)1929 3209 y Fk(1)1898 3267 y Ft(1)1968 3243 y Fw(t)2003 3200 y Fv(c)2034 3209 y Fk(2)2003 3267 y Ft(2)2089 3243 y Fw(:)17 b(:)g(:)f(t)2255 3198 y Fv(c)2286 3209 y Fl(P)2255 3270 y Fv(P)2341 3243 y Fy(\))47 b(=)f Fw(\013)2610 3258 y Fv(c)2645 3243 y Fw(L)p Fy(\()p Fw(c)p Fy(\))30 b Fx(\012)g Fy(1)47 b Fx(2)3192 3217 y Fn(e)3175 3243 y Fj(B)p Fy(\()p Fw(W)14 b Fy(\))3445 3258 y Fh(|)3486 3243 y Fy(,)46 b(where)g Fw(\013)3915 3258 y Fv(c)3996 3243 y Fy(=)-180 3383 y Fw(')-99 3302 y Fn(\000)-54 3308 y(Q)40 3412 y Ft(1)p Fu(\024)p Fv(s)p Fu(\024)p Fv(P)277 3383 y Fy(\([)p Fw(c)384 3398 y Fv(s)420 3383 y Fy(])447 3398 y Fv(i)471 3406 y Fl(s)509 3383 y Fy(!\))574 3346 y Fu(\000)p Ft(1)668 3302 y Fn(\001)765 3383 y Fy(is)51 b(a)g(non-zero)g(scalar)g(in)f Fo(|)-8 b Fy(.)93 b(Cho)s(ose)52 b(elemen)m(ts)2785 3356 y Fn(e)2782 3383 y Fw(`)p Fy(\()p Fw(c)p Fy(\))59 b Fx(2)h Fw(T)14 b Fy(\()p Fw(V)21 b Fy(\))51 b(with)i Fn(e)-57 b Fw(\031)t Fy(\()3744 3356 y Fn(e)3740 3383 y Fw(`)p Fy(\()p Fw(c)p Fy(\)\))59 b(=)-172 3504 y Fn(e)-180 3529 y Fw(L)p Fy(\()p Fw(c)p Fy(\))31 b Fx(\012)g Fy(1,)48 b Fw(c)h Fx(2)g Fo(N)539 3493 y Fv(P)603 3529 y Fy(.)81 b(Then)46 b(for)f(all)e Fw(c;)17 b(c)1416 3493 y Fu(0)1487 3529 y Fx(2)50 b Fo(N)1668 3493 y Fv(P)1733 3529 y Fy(,)e(w)m(e)e(conclude)g(that)f(\()p Fw(t)2675 3486 y Fv(c)2706 3495 y Fk(1)2675 3554 y Ft(1)2744 3529 y Fw(t)2779 3486 y Fv(c)2810 3495 y Fk(2)2779 3554 y Ft(2)2865 3529 y Fw(:)17 b(:)g(:)f(t)3031 3484 y Fv(c)3062 3495 y Fl(P)3031 3556 y Fv(P)3117 3529 y Fx(j)3149 3503 y Fn(e)3145 3529 y Fw(`)p Fy(\()p Fw(c)3266 3493 y Fu(0)3289 3529 y Fy(\)\))49 b(=)f(0,)g(if)c Fw(c)49 b Fx(6)p Fy(=)g Fw(c)4022 3493 y Fu(0)4045 3529 y Fy(,)-180 3669 y(and)e(\()p Fw(t)97 3625 y Fv(c)128 3634 y Fk(1)97 3693 y Ft(1)167 3669 y Fw(t)202 3625 y Fv(c)233 3634 y Fk(2)202 3693 y Ft(2)288 3669 y Fw(:)17 b(:)g(:)f(t)454 3623 y Fv(c)485 3634 y Fl(P)454 3696 y Fv(P)540 3669 y Fx(j)572 3643 y Fn(e)568 3669 y Fw(`)p Fy(\()p Fw(c)p Fy(\)\))52 b Fx(6)p Fy(=)g(0.)87 b(Since)47 b(the)g(form)f(\()98 b Fx(j)f Fy(\))47 b(factorizes)g(o)m(v)m(er)h Fj(B)p Fy(\()p Fw(V)21 b Fy(\))32 b Fx(\002)h Fj(B)p Fy(\()p Fw(V)21 b Fy(\),)51 b(the)d(elemen)m(ts)-180 3808 y Fw(b)-139 3765 y Fv(c)-108 3774 y Fk(1)-139 3833 y Ft(1)-69 3808 y Fw(b)-28 3765 y Fv(c)3 3774 y Fk(2)-28 3833 y Ft(2)58 3808 y Fw(:)17 b(:)g(:)f(b)230 3763 y Fv(c)261 3774 y Fl(P)230 3835 y Fv(P)317 3808 y Fy(,)32 b Fw(c)418 3823 y Ft(1)458 3808 y Fw(;)17 b(:)g(:)g(:)e(;)i(c)718 3823 y Fv(P)804 3808 y Fx(\025)29 b Fy(0,)j(are)h(linearly)d(indep)s(enden)m (t.)-80 3992 y(The)j(follo)m(wing)d(statemen)m(t)j(is)f(w)m(ell-kno)m (wn:)-80 4132 y(Let)41 b Fw(A)f Fy(b)s(e)h(a)g Fw(k)s Fy(-algebra,)g(where)h Fw(k)i Fy(is)c(a)h(\014eld.)67 b(Let)41 b Fw(a)2000 4147 y Ft(1)2040 4132 y Fw(;)17 b(:)g(:)g(:)f(;)h(a)2310 4147 y Fv(P)2410 4132 y Fx(2)42 b Fw(A)f Fy(suc)m(h)h(that)f(the)g(ordered)g(monomials)-180 4271 y Fw(a)-129 4228 y Fv(c)-98 4237 y Fk(1)-129 4296 y Ft(1)-59 4271 y Fw(a)-8 4228 y Fv(c)23 4237 y Fk(2)-8 4296 y Ft(2)78 4271 y Fw(:)17 b(:)g(:)f(a)260 4226 y Fv(c)291 4237 y Fl(P)260 4298 y Fv(P)346 4271 y Fy(,)35 b Fw(c)450 4286 y Ft(1)490 4271 y Fw(;)17 b(:)g(:)g(:)e(;)i(c)750 4286 y Fv(P)840 4271 y Fx(\025)32 b Fy(0,)j(are)g(linearly)e(indep)s (enden)m(t.)51 b(Then)36 b(the)f(Gelfand-Kirillo)m(v)30 b(dimension)j(of)i Fw(A)f Fy(is)-180 4411 y Fx(\025)28 b Fw(P)14 b Fy(.)-80 4550 y(W)-8 b(e)37 b(conclude)h(that)f(the)h (Gelfand-Kirillo)m(v)32 b(dimension)k(of)h Fj(B)p Fy(\()p Fw(V)22 b Fy(\))37 b(is)g Fx(\025)f Fw(P)14 b Fy(.)57 b(If)38 b(the)f(Cartan)h(matrix)d(\()p Fw(a)3870 4565 y Fv(ij)3931 4550 y Fy(\))i(is)-180 4690 y(not)32 b(\014nite,)h(then)g (there)g(are)g(elemen)m(ts)g(in)f(the)h(W)-8 b(eyl)32 b(group)h(of)f(arbitrary)f(lengh)m(t,)i(and)f(\(i\))g(follo)m(ws.)-80 4874 y(\(ii\).)79 b(No)m(w)45 b(the)h(W)-8 b(eyl)45 b(group)g(is)f (\014nite,)k(and)d(w)m(e)h(tak)m(e)g(the)g(longest)e(elemen)m(t)h Fw(w)3072 4889 y Ft(0)3111 4874 y Fy(.)81 b(Let)45 b(us)h(consider)f (the)-180 5013 y(natural)35 b(map)g Fw(')e Fy(:)h Fo(|)-9 b Fx(h)p Fw(x)698 5028 y Ft(1)731 5013 y Fw(;)17 b(:)g(:)g(:)f(;)h(x) 1005 5028 y Fv(\022)1044 5013 y Fx(j)p Fy(ad)1191 5028 y Fv(c)1226 5013 y Fy(\()p Fw(x)1319 5028 y Fv(i)1348 5013 y Fy(\))1386 4977 y Ft(1)p Fu(\000)p Fv(a)1513 4987 y Fl(ij)1572 5013 y Fw(;)g Fy(1)27 b Fx(\024)h Fw(i)g Fx(6)p Fy(=)g Fw(j)34 b Fx(\024)28 b Fw(\022)s Fx(i)33 b(!)g Fj(B)p Fy(\()p Fw(V)21 b Fy(\).)54 b(Since)36 b(the)g(elemen)m (ts)g Fw(b)3589 4969 y Fv(c)3620 4978 y Fk(1)3589 5037 y Ft(1)3659 5013 y Fw(b)3700 4969 y Fv(c)3731 4978 y Fk(2)3700 5037 y Ft(2)3786 5013 y Fw(:)17 b(:)g(:)g(b)3959 4968 y Fv(c)3990 4979 y Fl(P)3959 5040 y Fv(P)4045 5013 y Fy(,)-180 5152 y Fw(c)-138 5167 y Ft(1)-99 5152 y Fw(;)g(:)g(:)g(:)f (;)h(c)162 5167 y Fv(P)250 5152 y Fx(\025)29 b Fy(0,)34 b(are)f(the)h(image)e(of)h(the)h(PBW-basis)f(of)g Fo(|)-8 b Fx(h)p Fw(x)2138 5167 y Ft(1)2171 5152 y Fw(;)17 b(:)g(:)g(:)f(;)h(x) 2445 5167 y Fv(\022)2484 5152 y Fx(j)p Fy(ad)2631 5167 y Fv(c)2666 5152 y Fy(\()p Fw(x)2759 5167 y Fv(i)2788 5152 y Fy(\))2826 5116 y Ft(1)p Fu(\000)p Fv(a)2953 5126 y Fl(ij)3012 5152 y Fw(;)g Fy(1)27 b Fx(\024)h Fw(i)g Fx(6)p Fy(=)g Fw(j)33 b Fx(\024)c Fw(\022)s Fx(i)p Fy(,)k(see)i Fs(e.)g(g.)-180 5292 y Fy([DCK,)d(Prop)s(osition)f(1.7],)i(the)g(claim) d(follo)m(ws.)2386 b Fi(\003)p eop %%Page: 10 10 10 9 bop -180 0 a Fp(10)846 b(NICOL)1001 -19 y(\023)991 0 y(AS)24 b(ANDR)n(USKIEWITSCH)f(AND)h(HANS-J)2419 -19 y(\177)2409 0 y(UR)n(GEN)f(SCHNEIDER)-180 203 y FC(Rosso's)38 b(c)m(haracterization)e(of)h(Nic)m(hols)f(algebras.)49 b Fy(W)-8 b(e)33 b(recall)e(some)i(imp)s(ortan)m(t)d(results)j(of)f (Rosso.)-180 364 y FC(Theorem)38 b(2.11.)k Fy([Ro,)34 b(Lemma)e(19])j Fs(L)-5 b(et)36 b Fy(\()p Fw(V)5 b(;)17 b(c)p Fy(\))36 b Fs(b)-5 b(e)35 b(a)h(br)-5 b(aide)g(d)35 b(ve)-5 b(ctor)35 b(sp)-5 b(ac)g(e)35 b(of)g(diagonal)g(typ)-5 b(e.)47 b(If)35 b Fj(B)p Fy(\()p Fw(V)22 b Fy(\))35 b Fs(has)-180 503 y(\014nite)25 b(Gelfand-Kiril)5 b(lov)24 b(dimension,)i(then)g(for)f(al)5 b(l)25 b Fw(i)j Fx(6)p Fy(=)g Fw(j)6 b Fs(,)27 b(ther)-5 b(e)26 b(exists)f Fw(r)30 b(>)e Fy(0)d Fs(such)h(that)g Fy(ad)3285 518 y Fv(c)3320 503 y Fy(\()p Fw(x)3413 518 y Fv(i)3441 503 y Fy(\))3479 467 y Fv(r)3517 503 y Fy(\()p Fw(x)3610 518 y Fv(j)3647 503 y Fy(\))i(=)f(0)p Fs(.)99 b Fi(\003)-180 706 y FC(Corollary)44 b(2.12.)g Fs(L)-5 b(et)40 b Fy(\()p Fw(V)5 b(;)17 b(c)p Fy(\))40 b Fs(b)-5 b(e)40 b(a)f(br)-5 b(aide)g(d)39 b(ve)-5 b(ctor)40 b(sp)-5 b(ac)g(e)39 b(of)h(diagonal)e(typ)-5 b(e)40 b(with)g(inde)-5 b(c)g(omp)g(osable)37 b(matrix.)-180 845 y(Assume)e(that)g Fj(B)p Fy(\()p Fw(V)22 b Fy(\))34 b Fs(has)h(\014nite)f(Gelfand-Kiril)5 b(lov)34 b(dimension.)-80 985 y(\(a\).)44 b(If)34 b(ther)-5 b(e)35 b(exists)g Fw(i)g Fs(such)f(that)i Fw(q)1268 1000 y Fv(ii)1348 985 y Fy(=)27 b(1)p Fs(,)35 b(then)f Fw(\022)d Fy(=)d(1)p Fs(.)-80 1124 y(\(b\).)44 b(If)34 b(the)h(br)-5 b(aiding)34 b(is)h(generic)f (then)g(it)h(is)g(of)g(Cartan)f(typ)-5 b(e.)-180 1316 y(Pr)g(o)g(of.)41 b Fy(This)33 b(follo)m(ws)e(from)g(Theorem)i(2.11)f (and)h(Lemma)e(2.1)h(\(e\).)1644 b Fi(\003)-180 1507 y FC(Theorem)28 b(2.13.)36 b Fy([Ro)o(,)26 b(Theorem)f(21])i Fs(L)-5 b(et)28 b Fy(\()p Fw(V)5 b(;)17 b(c)p Fy(\))27 b Fs(b)-5 b(e)27 b(a)h(\014nite-dimensional)d(br)-5 b(aide)g(d)26 b(ve)-5 b(ctor)28 b(sp)-5 b(ac)g(e)26 b(with)i(p)-5 b(ositive)-180 1646 y(br)g(aiding.)44 b(Then)34 b(the)h(fol)5 b(lowing)33 b(ar)-5 b(e)35 b(e)-5 b(quivalent:)-80 1786 y(\(a\).)44 b Fj(B)p Fy(\()p Fw(V)21 b Fy(\))35 b Fs(has)g(\014nite)f (Gelfand-Kiril)5 b(lov)34 b(dimension.)-80 1925 y(\(b\).)44 b Fy(\()p Fw(V)5 b(;)17 b(c)p Fy(\))35 b Fs(is)f(twist-e)-5 b(quivalent)35 b(to)g(a)f(br)-5 b(aiding)34 b(of)h(DJ-typ)-5 b(e)35 b(with)f(\014nite)h(Cartan)f(matrix.)-180 2116 y(Pr)-5 b(o)g(of.)41 b Fy(W)-8 b(e)34 b(can)h(assume)f(that)g(the)g (matrix)f(\()p Fw(q)1588 2131 y Fv(ij)1648 2116 y Fy(\))h(is)g (indecomp)s(osable.)46 b(\(b\))64 b(=)-17 b Fx(\))64 b Fy(\(a\))33 b(follo)m(ws)g(from)g(Theorem)-180 2256 y(2.10)g(\(ii\).)44 b(\(a\))63 b(=)-17 b Fx(\))63 b Fy(\(b\).)46 b(\()p Fw(V)5 b(;)17 b(c)p Fy(\))34 b(is)f(of)g(Cartan)g(t)m(yp)s(e)i (b)m(y)f(Corollary)e(2.12)h(\(b\))h(with)f(Cartan)g(matrix)f(\()p Fw(a)3764 2271 y Fv(ij)3825 2256 y Fy(\).)47 b(W)-8 b(e)-180 2395 y(kno)m(w)37 b(that)f(\()p Fw(a)382 2410 y Fv(ij)443 2395 y Fy(\))f(is)h(symmetrizable)e(b)m(y)j(Lemma)e(2.4)g(and)h(that)g (\()p Fw(V)5 b(;)17 b(c)p Fy(\))36 b(is)f(t)m(wist-equiv)-5 b(alen)m(t)36 b(to)g(a)f(braiding)f(of)-180 2535 y(DJ-t)m(yp)s(e)f(b)m (y)g(Lemma)e(2.5.)43 b(By)33 b(Theorem)g(2.10)f(\(i\),)g(the)h(Cartan)f (matrix)f(\()p Fw(a)2713 2550 y Fv(ij)2774 2535 y Fy(\))i(is)f (\014nite.)807 b Fi(\003)-180 2726 y FC(Remark)51 b(2.14.)d Fy(See)d([AS2)q(])f(for)g(the)i(analogous)d(problem)h(of)g(c)m (haracterizing)g(\014nite-dimensional)d(braided)-180 2865 y(v)m(ector)34 b(spaces)g(with)e(diagonal)e(braiding)h(suc)m(h)j (that)e Fj(B)p Fy(\()p Fw(V)22 b Fy(\))32 b(has)h(\014nite)g (dimension.)1060 3091 y(3.)48 b Fz(Coradicall)-7 b(y)40 b(graded)d(co)n(algebras)-80 3265 y Fy(In)h(this)g(Section)g(w)m(e)h (pro)m(v)m(e)g(a)f(general)f(criterion)g(to)g(determine)h(the)h (coradical)d(\014ltration)g(of)h(certain)h(Hopf)-180 3381 y(algebras.)k(W)-8 b(e)31 b(generalize)g(a)f(metho)s(d)g(of)h(T)-8 b(ak)m(euc)m(hi)32 b([T],)g(who)f(computed)g(the)g(coradical)e (\014ltration)g(of)h Fw(U)3795 3396 y Fv(q)3834 3381 y Fy(\()p Fw(g)t Fy(\))g(in)-180 3497 y(this)i(w)m(a)m(y;)i(see)g(also) d([Mu)q(].)44 b(W)-8 b(e)33 b(\014rst)g(extend)h(the)f(de\014nition)e (of)h(coradically)f(graded)i(coalgebras)f([CM)q(].)-80 3656 y(Let)g Fw(T)42 b Fx(\025)28 b Fy(1)k(b)s(e)h(a)f(natural)g(n)m (um)m(b)s(er.)44 b(If)32 b FC(i)27 b Fy(=)h(\()p Fw(i)1659 3671 y Ft(1)1698 3656 y Fw(;)17 b(:)g(:)g(:)f(;)h(i)1950 3671 y Fv(T)2005 3656 y Fy(\))28 b Fx(2)g Fo(N)2231 3620 y Fv(T)2292 3656 y Fy(,)k(then)h(w)m(e)h(set)f Fx(j)p FC(i)p Fx(j)27 b Fy(=)g Fw(i)3120 3671 y Ft(1)3182 3656 y Fy(+)22 b Fx(\001)17 b(\001)g(\001)j Fy(+)i Fw(i)3549 3671 y Fv(T)3605 3656 y Fy(.)-180 3817 y FC(De\014nition)56 b(3.1.)50 b Fy(An)100 b Fo(N)880 3780 y Fv(T)941 3817 y Fs(-gr)-5 b(ade)g(d)50 b(c)-5 b(o)g(algebr)g(a)56 b Fy(is)49 b(a)g(coalgebra)g Fw(C)56 b Fy(pro)m(vided)50 b(with)f(an)h Fo(N)3400 3780 y Fv(T)3461 3817 y Fy(-grading)e Fw(C)63 b Fy(=)-180 3956 y Fx(\010)-103 3975 y Ff(i)p Fu(2)p Fh(N)11 3956 y Fl(T)21 b Fw(C)7 b Fy(\()p FC(i)p Fy(\))31 b(suc)m(h)j(that)f(\001)p Fw(C)7 b Fy(\()p FC(i)p Fy(\))27 b Fx(\032)h(\010)1191 3971 y Ff(j)1220 3956 y Fw(C)7 b Fy(\()p FC(j)p Fy(\))23 b Fx(\012)f Fw(C)7 b Fy(\()p FC(i)21 b Fx(\000)i FC(j)p Fy(\).)44 b(An)33 b Fo(N)2166 3920 y Fv(T)2227 3956 y Fy(-graded)f(coalgebra)f Fw(C)40 b Fy(is)32 b Fs(c)-5 b(or)g(adic)g(al)5 b(ly)34 b(gr)-5 b(ade)g(d)42 b Fy(if)-180 4095 y(the)33 b Fw(n)p Fy(-th)f(term)g(of)h(the)g(coradical)d(\014ltration)h(is)1279 4277 y Fw(C)1349 4292 y Fv(n)1423 4277 y Fy(=)d Fx(\010)1604 4296 y Ff(i)p Fu(2)p Fh(N)1718 4277 y Fl(T)1770 4296 y Fv(;)p Fu(j)p Ff(i)p Fu(j\024)p Fv(n)1954 4277 y Fw(C)7 b Fy(\()p FC(i)p Fy(\))p Fw(;)113 b Fx(8)p Fw(n)28 b Fx(2)g Fo(N)9 b Fw(:)-80 4459 y Fy(W)-8 b(e)33 b(denote)g(b)m(y)g Fw(\031)592 4474 y Ff(i)647 4459 y Fy(:)28 b Fw(C)35 b Fx(!)27 b Fw(C)7 b Fy(\()p FC(i)p Fy(\))31 b(the)i(pro)5 b(jection)33 b(asso)s(ciated)f(to)g(the)h(grading.)-80 4598 y(An)42 b Fo(N)155 4562 y Fv(T)216 4598 y Fy(-graded)g(coalgebra)g Fw(C)49 b Fy(is)42 b Fs(strictly)i(c)-5 b(or)g(adic)g(al)5 b(ly)43 b(gr)-5 b(ade)g(d)52 b Fy(if)41 b Fw(C)7 b Fy(\(0\))44 b(=)h Fw(C)2935 4613 y Ft(0)2974 4598 y Fy(,)g(the)d(coradical)f(of)h Fw(C)7 b Fy(,)45 b(and)-180 4738 y(\001)-99 4753 y Ff(i)p Fv(;)p Ff(j)0 4738 y Fy(:)28 b Fw(C)7 b Fy(\()p FC(i)21 b Fy(+)h FC(j)p Fy(\))28 b Fx(!)f Fw(C)7 b Fy(\()p FC(i)p Fy(\))21 b Fx(\012)i Fw(C)7 b Fy(\()p FC(j)p Fy(\),)33 b(\001)1182 4753 y Ff(i)p Fv(;)p Ff(j)1281 4738 y Fy(=)27 b(\()p Fw(\031)1477 4753 y Ff(i)1527 4738 y Fx(\012)22 b Fw(\031)1681 4753 y Ff(j)1711 4738 y Fy(\))g Fx(\016)g Fy(\001,)32 b(is)h(injectiv)m(e,)f(for)g(all)f FC(i)p Fw(;)17 b FC(j)26 b Fx(2)j Fo(N)3077 4702 y Ff(T)3144 4738 y Fy(.)-180 4898 y FC(Lemma)37 b(3.2.)k Fs(\(a\).)j(L)-5 b(et)35 b Fw(C)41 b Fs(b)-5 b(e)34 b(a)h(strictly)g(c)-5 b(or)g(adic)g(al)5 b(ly)33 b Fo(N)1993 4862 y Fv(T)2054 4898 y Fs(-gr)-5 b(ade)g(d)34 b(c)-5 b(o)g(algebr)g(a)33 b(and)h(let)g Fw(D)j Fs(b)-5 b(e)34 b(a)h(strictly)g(c)-5 b(or)g(adi-)-180 5038 y(c)g(al)5 b(ly)34 b Fo(N)112 5002 y Fv(S)168 5038 y Fs(-gr)-5 b(ade)g(d)33 b(c)-5 b(o)g(algebr)g(a.)44 b(Then)33 b Fw(C)26 b Fx(\012)21 b Fw(D)36 b Fs(is)e(strictly)h(c)-5 b(or)g(adic)g(al)5 b(ly)33 b Fo(N)2503 5002 y Fv(T)11 b Ft(+)p Fv(S)2666 5038 y Fs(-gr)-5 b(ade)g(d)33 b(with)h(r)-5 b(esp)g(e)g(ct)33 b(to)h(the)g(tensor)-180 5177 y(pr)-5 b(o)g(duct)35 b(gr)-5 b(ading.)-80 5317 y(\(b\).)44 b(If)34 b Fw(C)42 b Fs(is)35 b(strictly)g(c)-5 b(or)g(adic)g(al)5 b(ly)34 b Fo(N)1313 5281 y Fv(T)1374 5317 y Fs(-gr)-5 b(ade)g(d,)34 b(then)h(it)g(is)f(c)-5 b(or)g(adic)g(al)5 b(ly)34 b(gr)-5 b(ade)g(d.)p eop %%Page: 11 11 11 10 bop 1010 0 a Fp(A)33 b(CHARA)n(CTERIZA)-6 b(TION)31 b(OF)i(QUANTUM)f(GR)n(OUPS)1112 b(11)-80 203 y Fs(\(c\).)44 b(If)34 b Fw(C)42 b Fs(is)35 b(c)-5 b(or)g(adic)g(al)5 b(ly)34 b Fo(N)9 b Fs(-gr)-5 b(ade)g(d,)39 b(then)c(it)g(is)g(strictly) g(c)-5 b(or)g(adic)g(al)5 b(ly)34 b(gr)-5 b(ade)g(d.)-180 397 y(Pr)g(o)g(of.)41 b Fy(\(a\))32 b(follo)m(ws)f(from)g(the)h (de\014nition.)42 b(W)-8 b(e)33 b(pro)m(v)m(e)g(\(b\))g(b)m(y)g (induction)e(on)h Fw(n)p Fy(,)g(the)h(case)g Fw(n)28 b Fy(=)f(0)32 b(b)s(eing)f(part)h(of)-180 536 y(the)c(h)m(yp)s (othesis.)43 b(Assume)28 b Fw(n)g(>)g Fy(0.)41 b(If)28 b Fw(c)g Fx(2)g(\010)1497 552 y Fu(j)p Ff(i)p Fu(j\024)p Fv(n)1661 536 y Fw(C)7 b Fy(\()p FC(i)p Fy(\),)27 b(then)i(\001\()p Fw(c)p Fy(\))f Fx(2)g Fw(C)7 b Fy(\()p FC(0)p Fy(\))12 b Fx(\012)g Fw(C)7 b Fy(\()p FC(n)p Fy(\))12 b(+)g Fx(\010)3141 552 y Fu(j)p Ff(j)p Fu(j)p Fv()i(n)p Fy(.)42 b(By)30 b(the)h(recursiv)m(e)g(h)m(yp)s(othesis,)g (\001\()p Fw(c)p Fy(\))d Fx(2)g Fw(C)7 b Fy(\()p FC(0)p Fy(\))16 b Fx(\012)g Fw(C)24 b Fy(+)16 b Fx(\010)3242 831 y Fu(j)p Ff(j)p Fu(j)p Fv()27 b Fy(0,)32 b(for)g(all)f Fw(I)k Fx(2)29 b(X)15 b Fy(.)-80 1190 y(Let)30 b Fx(D)172 1154 y Fu(0)226 1190 y Fy(b)s(e)g(a)h(generic)f(datum)g(of)g(\014nite)g(Cartan)h(t)m(yp)s(e) g(o)m(v)m(er)h(a)e(free)h(ab)s(elian)e(group)h(\000)3116 1154 y Fu(0)3170 1190 y Fy(of)g(\014nite)g(rank,)i(formed)-180 1330 y(b)m(y)c(\()p Fw(a)39 1294 y Fu(0)39 1354 y Fv(ij)99 1330 y Fy(\))g Fx(2)g Fo(Z)328 1294 y Fv(\022)363 1270 y Fg(0)383 1294 y Fu(\002)p Fv(\022)473 1270 y Fg(0)499 1330 y Fy(,)g(\()p Fw(q)639 1294 y Fu(0)635 1355 y Fv(I)675 1330 y Fy(\))713 1345 y Fv(I)5 b Fu(2X)856 1326 y Fg(0)883 1330 y Fy(,)28 b Fw(g)989 1294 y Fu(0)985 1354 y Ft(1)1024 1330 y Fw(;)17 b(:)g(:)g(:)f(;)h(g)1294 1294 y Fu(0)1290 1356 y Fv(\022)1328 1330 y Fy(,)28 b Fw(\037)1444 1294 y Fu(0)1444 1354 y Ft(1)1484 1330 y Fw(;)17 b(:)g(:)g(:)e(;)i(\037)1763 1294 y Fu(0)1763 1356 y Fv(\022)1829 1330 y Fy(and)27 b(a)g(linking)e(datum)h(\()p Fw(\025)2804 1294 y Fu(0)2804 1354 y Fv(ij)2864 1330 y Fy(\))2902 1345 y Ft(1)p Fu(\024)p Fv(i)g(\033)t Fy(\()p Fw(j)6 b Fy(\))2036 2184 y(,)32 b(for)h(all)d(1)d Fx(\024)i Fw(i)f(<)f(j)34 b Fx(\024)28 b Fw(\022)s(;)17 b(i)28 b Fo(\034)g Fw(j:)-180 2459 y Fy(In)33 b(this)f(case)i(the)f (triple)e(\()p Fw(';)17 b(\033)n(;)g Fy(\()p Fw(\013)1110 2474 y Fv(i)1138 2459 y Fy(\)\))32 b(will)e(b)s(e)j(called)f(an)g Fs(isomorphism)f Fy(from)g Fx(D)k Fy(to)d Fx(D)3088 2423 y Fu(0)3111 2459 y Fy(.)-80 2598 y(Note)37 b(that)f(then)i Fw(a)653 2613 y Fv(ij)749 2598 y Fy(=)d Fw(a)911 2562 y Fu(0)911 2628 y Fv(\033)r Ft(\()p Fv(i)p Ft(\))p Fv(\033)r Ft(\()p Fv(j)t Ft(\))1167 2598 y Fy(,)j(for)e(all)f(1)g Fx(\024)g Fw(i;)17 b(j)41 b Fx(\024)36 b Fw(\022)s Fy(.)57 b(Th)m(us)38 b Fw(\033)j Fy(is)36 b(an)h(isomorphism)e(of)h(the)i (corresp)s(ond-)-180 2738 y(ing)45 b(Dynkin)g(diagrams.)81 b(Indeed,)50 b(for)45 b(all)f Fw(i;)17 b(j)6 b Fy(,)49 b Fw(\037)1780 2753 y Fv(j)1816 2738 y Fy(\()p Fw(g)1901 2753 y Fv(i)1929 2738 y Fy(\))h(=)f Fw(\037)2203 2702 y Fu(0)2203 2767 y Fv(\033)r Ft(\()p Fv(i)p Ft(\))2329 2738 y Fy(\()p Fw(g)2418 2702 y Fu(0)2414 2767 y Fv(\033)r Ft(\()p Fv(i)p Ft(\))2540 2738 y Fy(\),)g(hence)e Fw(\037)2999 2753 y Fv(j)3035 2738 y Fy(\()p Fw(g)3120 2753 y Fv(i)3148 2738 y Fy(\))p Fw(\037)3247 2753 y Fv(i)3275 2738 y Fy(\()p Fw(g)3360 2753 y Fv(j)3396 2738 y Fy(\))j(=)g Fw(\037)3671 2753 y Fv(i)3699 2738 y Fy(\()p Fw(g)3784 2753 y Fv(i)3812 2738 y Fy(\))3850 2702 y Fv(a)3887 2712 y Fl(ij)3996 2738 y Fy(=)-180 2893 y Fw(\037)-119 2908 y Fv(i)-91 2893 y Fy(\()p Fw(g)-6 2908 y Fv(i)22 2893 y Fy(\))60 2844 y Fv(a)97 2820 y Fg(0)97 2869 y Fl(\033)r Fk(\()p Fl(i)p Fk(\))p Fl(\033)r Fk(\()p Fl(j)s Fk(\))327 2893 y Fy(,)33 b(and)g Fw(a)628 2908 y Fv(ij)716 2893 y Fy(=)28 b Fw(a)871 2856 y Fu(0)871 2922 y Fv(\033)r Ft(\()p Fv(i)p Ft(\))p Fv(\033)r Ft(\()p Fv(j)t Ft(\))1127 2893 y Fy(,)k(since)h Fw(\037)1486 2908 y Fv(i)1514 2893 y Fy(\()p Fw(g)1599 2908 y Fv(i)1627 2893 y Fy(\))g(is)f(not)g(a)g(ro)s(ot)g(of)g(1.)-80 3032 y(Let)g(Isom\()p Fx(D)s Fw(;)17 b Fx(D)540 2996 y Fu(0)562 3032 y Fy(\))33 b(b)s(e)g(the)g(set)g(of)f(all)e (isomorphisms)h(from)g Fx(D)k Fy(to)e Fx(D)2483 2996 y Fu(0)2506 3032 y Fy(.)-80 3299 y(T)-8 b(o)40 b(state)h(the)f(next)i (theorem,)g(w)m(e)f(follo)m(w)d(the)j(con)m(v)m(en)m(tions)h(of)e ([AS4,)i(Section)f(4].)66 b(W)-8 b(e)41 b(assume)f(that)g(the)-180 3415 y(Cartan)f(matrix)e(is)h(a)g(matrix)f(of)h(blo)s(c)m(ks)h(corresp) s(onding)g(to)f(the)h(connected)i(comp)s(onen)m(ts;)h(that)c(is,)i(for) e(eac)m(h)-180 3531 y Fw(I)e Fx(2)28 b(X)15 b Fy(,)32 b(there)h(exist)g Fw(c)660 3546 y Fv(I)700 3531 y Fw(;)17 b(d)795 3546 y Fv(I)867 3531 y Fy(suc)m(h)34 b(that)e Fw(I)k Fy(=)27 b Fx(f)p Fw(j)34 b Fy(:)27 b Fw(c)1700 3546 y Fv(I)1768 3531 y Fx(\024)h Fw(j)34 b Fx(\024)28 b Fw(d)2103 3546 y Fv(I)2143 3531 y Fx(g)p Fy(.)-80 3647 y(Let)41 b(\010)173 3662 y Fv(I)213 3647 y Fy(,)i(resp.)70 b(\010)623 3606 y Ft(+)623 3674 y Fv(I)682 3647 y Fy(,)43 b(b)s(e)e(the)h(ro)s(ot)d(system,)45 b(resp.)69 b(the)41 b(subset)i(of)d(p)s(ositiv)m(e)g(ro)s(ots,)j(corresp)s(onding)e(to)f (the)-180 3764 y(Cartan)i(matrix)f(\()p Fw(a)576 3779 y Fv(ij)637 3764 y Fy(\))675 3779 y Fv(i;j)t Fu(2)p Fv(I)838 3764 y Fy(;)47 b(then)c(\010)i(=)1380 3689 y Fn(S)1463 3793 y Fv(I)5 b Fu(2X)1626 3764 y Fy(\010)1696 3779 y Fv(I)1737 3764 y Fy(,)45 b(resp.)74 b(\010)2153 3728 y Ft(+)2256 3764 y Fy(=)2377 3689 y Fn(S)2460 3793 y Fv(I)5 b Fu(2X)2623 3764 y Fy(\010)2693 3723 y Ft(+)2693 3791 y Fv(I)2795 3764 y Fy(is)42 b(the)h(ro)s(ot)f(system,)j(resp.)74 b(the)-180 3880 y(subset)33 b(of)d(p)s(ositiv)m(e)h(ro)s(ots,)g (corresp)s(onding)g(to)f(the)i(Cartan)f(matrix)f(\()p Fw(a)2503 3895 y Fv(ij)2563 3880 y Fy(\))2601 3895 y Ft(1)p Fu(\024)p Fv(i;j)t Fu(\024)p Fv(\022)2861 3880 y Fw(:)h Fy(Let)h Fw(\013)3155 3895 y Ft(1)3194 3880 y Fw(;)17 b(:)g(:)g(:)f(;)h(\013)3475 3895 y Fv(\022)3545 3880 y Fy(b)s(e)31 b(the)h(set)f(of)-180 3996 y(simple)g(ro)s(ots.)-80 4150 y(Let)47 b Fx(W)207 4165 y Fv(I)294 4150 y Fy(b)s(e)h(the)f(W)-8 b(eyl)47 b(group)g(corresp)s(onding)g(to)g(the)h(Cartan)f(matrix)e(\()p Fw(a)2899 4165 y Fv(ij)2960 4150 y Fy(\))2998 4165 y Fv(i;j)t Fu(2)p Fv(I)3161 4150 y Fy(;)54 b(w)m(e)49 b(iden)m(tify)d(it) g(with)-180 4267 y(a)h(subgroup)h(of)f(the)h(W)-8 b(eyl)48 b(group)f Fx(W)56 b Fy(corresp)s(onding)48 b(to)f(the)h(Cartan)f (matrix)f(\()p Fw(a)3095 4282 y Fv(ij)3156 4267 y Fy(\).)88 b(W)-8 b(e)48 b(\014x)g(a)f(reduced)-180 4383 y(decomp)s(osition)37 b(of)i(the)h(longest)e(elemen)m(t)h Fw(!)1527 4398 y Ft(0)p Fv(;I)1661 4383 y Fy(of)g Fx(W)1877 4398 y Fv(I)1956 4383 y Fy(in)f(terms)h(of)g(simple)f(re\015ections.)64 b(Then)40 b(w)m(e)g(obtain)e(a)-180 4499 y(reduced)44 b(decomp)s(osition)e(of)g(the)h(longest)g(elemen)m(t)g Fw(!)1920 4514 y Ft(0)2004 4499 y Fy(=)i Fw(s)2171 4514 y Fv(i)2195 4523 y Fk(1)2251 4499 y Fw(:)17 b(:)g(:)f(s)2428 4514 y Fv(i)2452 4525 y Fl(P)2550 4499 y Fy(of)42 b Fx(W)52 b Fy(from)42 b(the)h(expression)h(of)f Fw(!)3903 4514 y Ft(0)3985 4499 y Fy(as)-180 4615 y(pro)s(duct)34 b(of)g(the)g Fw(!)530 4630 y Ft(0)p Fv(;I)624 4615 y Fy('s)h(in)e(some)h(\014xed)h (order)f(of)f(the)h(comp)s(onen)m(ts,)h(sa)m(y)g(the)f(order)g(arising) e(from)h(the)h(order)g(of)-180 4731 y(the)f(v)m(ertices.)45 b(Therefore)33 b Fw(\014)875 4746 y Fv(j)940 4731 y Fy(:=)27 b Fw(s)1116 4746 y Fv(i)1140 4755 y Fk(1)1196 4731 y Fw(:)17 b(:)g(:)f(s)1373 4746 y Fv(i)1397 4756 y Fl(j)s Fg(\000)p Fk(1)1512 4731 y Fy(\()p Fw(\013)1612 4746 y Fv(i)1636 4756 y Fl(j)1673 4731 y Fy(\))32 b(is)g(a)g(n)m(umeration)g (of)g(\010)2621 4695 y Ft(+)2680 4731 y Fy(.)-80 4998 y(W)-8 b(e)29 b(\014x)h(a)f(\014nite-dimensional)d(Y)-8 b(etter-Drinfeld)27 b(mo)s(dule)h Fw(V)50 b Fy(o)m(v)m(er)30 b(\000)f(with)g(a)g(basis)g Fw(x)3086 5013 y Ft(1)3126 4998 y Fw(;)17 b(:)g(:)g(:)f(;)h(x)3400 5013 y Fv(\022)3468 4998 y Fy(with)29 b Fw(x)3742 5013 y Fv(i)3798 4998 y Fx(2)f Fw(V)3971 4962 y Fv(\037)4015 4972 y Fl(i)3949 5023 y Fv(g)3983 5033 y Fl(i)4045 4998 y Fy(,)-180 5114 y(1)f Fx(\024)i Fw(i)f Fx(\024)g Fw(\022)s Fy(.)43 b(Note)33 b(that)-180 5306 y(\(4.8\))949 b Fw(V)1048 5264 y Fv(\037)1092 5274 y Fl(i)1027 5330 y Fv(g)1061 5340 y Fl(i)1150 5306 y Fo(\035)28 b Fw(V)1334 5264 y Fv(\037)1378 5274 y Fl(j)1312 5330 y Fv(g)1346 5340 y Fl(j)1447 5306 y Fy(in)1561 5264 y Fh(|)-14 b Ft(\000)1561 5330 y Fh(|)g Ft(\000)1646 5306 y Fx(Y)8 b(D)r Fw(;)49 b Fy(for)32 b(all)f(1)c Fx(\024)i Fw(i;)17 b(j)33 b Fx(\024)28 b Fw(\022)s(;)17 b(i)28 b Fx(6)p Fy(=)g Fw(j:)p eop %%Page: 14 14 14 13 bop -180 0 a Fp(14)846 b(NICOL)1001 -19 y(\023)991 0 y(AS)24 b(ANDR)n(USKIEWITSCH)f(AND)h(HANS-J)2419 -19 y(\177)2409 0 y(UR)n(GEN)f(SCHNEIDER)-180 203 y Fy(F)-8 b(or)32 b(supp)s(ose)i(that)e Fw(V)652 167 y Fv(\037)696 177 y Fl(i)630 228 y Fv(g)664 238 y Fl(i)754 175 y Fx(\030)754 207 y Fy(=)859 203 y Fw(V)937 149 y Fv(\037)981 159 y Fl(j)916 213 y Fv(g)950 223 y Fl(j)1018 203 y Fy(,)g(and)h Fw(i)28 b Fx(6)p Fy(=)g Fw(j)6 b Fy(.)43 b(Then)34 b Fw(g)1850 218 y Fv(i)1905 203 y Fy(=)28 b Fw(g)2056 218 y Fv(j)2092 203 y Fy(,)33 b Fw(\037)2213 218 y Fv(i)2269 203 y Fy(=)27 b Fw(\037)2433 218 y Fv(j)2502 203 y Fy(and)1245 389 y Fw(\037)1306 404 y Fv(i)1334 389 y Fy(\()p Fw(g)1419 404 y Fv(i)1447 389 y Fy(\))1485 348 y Ft(2)1552 389 y Fy(=)h Fw(\037)1717 404 y Fv(i)1745 389 y Fy(\()p Fw(g)1830 404 y Fv(j)1866 389 y Fy(\))p Fw(\037)1965 404 y Fv(j)2002 389 y Fy(\()p Fw(g)2087 404 y Fv(i)2114 389 y Fy(\))g(=)g Fw(\037)2345 404 y Fv(i)2373 389 y Fy(\()p Fw(g)2458 404 y Fv(i)2486 389 y Fy(\))2524 348 y Fv(a)2561 358 y Fl(ij)2620 389 y Fw(:)-180 562 y Fy(Th)m(us)34 b Fw(a)118 577 y Fv(ij)207 562 y Fy(=)27 b(2,)32 b(since)h Fw(\037)718 577 y Fv(i)747 562 y Fy(\()p Fw(g)832 577 y Fv(i)860 562 y Fy(\))f(is)g(not)h(a)f(ro)s(ot)g(of)g(one;)h(but)f(this)h(is)f(a) g(con)m(tradiction.)-80 791 y(Lusztig)45 b(de\014ned)i(ro)s(ot)e(v)m (ectors)i Fw(X)1272 806 y Fv(\013)1322 791 y Fy(,)i Fw(\013)i Fx(2)f Fy(\010)1697 755 y Ft(+)1803 791 y Fy([L2)o(],)g(in)45 b(the)h(case)g(of)g(braidings)e(of)h(DJ-t)m(yp)s(e;)53 b(these)47 b(are)-180 907 y(the)e(elemen)m(ts)g Fw(b)452 922 y Ft(1)492 907 y Fw(;)17 b(:)g(:)g(:)f(;)h(b)752 922 y Fv(P)856 907 y Fy(in)44 b(the)h(pro)s(of)f(of)g(Theorem)h(2.10;) 51 b(they)45 b(can)g(b)s(e)g(expressed)j(as)d(iterated)f(braided)-180 1024 y(comm)m(utators.)d(As)30 b(in)e([AS4],)i(this)f(de\014nition)f (can)h(b)s(e)g(extended)i(to)e(generic)g(braidings)f(of)g(\014nite)h (Cartan)g(t)m(yp)s(e,)-180 1140 y(\014rst)k(in)f(the)h(tensor)g (algebra)e Fw(T)14 b Fy(\()p Fw(V)22 b Fy(\),)32 b(and)h(then)g(in)f (suitable)g(quotien)m(ts.)-80 1256 y(W)-8 b(e)33 b(\014x)g(a)f Fo(Z)p Fy(-basis)e Fw(Y)703 1271 y Fv(h)747 1256 y Fw(;)17 b Fy(1)27 b Fx(\024)h Fw(h)g Fx(\024)g Fw(s)33 b Fy(of)f(\000.)-180 1424 y FC(Theorem)45 b(4.2.)g Fs(L)-5 b(et)41 b Fx(D)h Fy(=)c Fx(D)s Fy(\(\()p Fw(a)1136 1439 y Fv(ij)1197 1424 y Fy(\))p Fw(;)17 b Fy(\()p Fw(q)1360 1439 y Fv(I)1399 1424 y Fy(\))p Fw(;)g Fy(\()p Fw(g)1566 1439 y Fv(i)1594 1424 y Fy(\))p Fw(;)g Fy(\()p Fw(\037)1775 1439 y Fv(i)1803 1424 y Fy(\))p Fw(;)g Fy(\()p Fw(\025)1980 1439 y Fv(ij)2040 1424 y Fy(\)\))41 b Fs(b)-5 b(e)40 b(a)h(generic)f(datum)h(of)g (\014nite)f(Cartan)h(typ)-5 b(e)41 b(for)-180 1563 y(the)e(fr)-5 b(e)g(e)40 b(ab)-5 b(elian)38 b(gr)-5 b(oup)39 b Fy(\000)h Fs(of)f(\014nite)g(r)-5 b(ank.)58 b(L)-5 b(et)40 b Fw(U)10 b Fy(\()p Fx(D)s Fy(\))39 b Fs(b)-5 b(e)39 b(the)h(algebr)-5 b(a)39 b(pr)-5 b(esente)g(d)38 b(by)i(gener)-5 b(ators)39 b Fw(a)3694 1578 y Ft(1)3733 1563 y Fw(;)17 b(:)g(:)g(:)f(;)h(a)4003 1578 y Fv(\022)4042 1563 y Fs(,)-180 1703 y Fw(y)-128 1662 y Fu(\006)p Ft(1)-132 1727 y(1)-35 1703 y Fw(;)g(:)g(:)g(:)f(;)h (y)236 1667 y Fu(\006)p Ft(1)232 1727 y Fv(s)364 1703 y Fs(and)35 b(r)-5 b(elations)1081 1899 y Fw(y)1133 1858 y Fu(\006)p Ft(1)1129 1923 y Fv(m)1227 1899 y Fw(y)1279 1857 y Fu(\006)p Ft(1)1275 1926 y Fv(h)1400 1899 y Fy(=)27 b Fw(y)1555 1857 y Fu(\006)p Ft(1)1551 1926 y Fv(h)1649 1899 y Fw(y)1701 1858 y Fu(\006)p Ft(1)1697 1923 y Fv(m)1794 1899 y Fw(;)117 b(y)1990 1858 y Fu(\006)p Ft(1)1986 1923 y Fv(m)2083 1899 y Fw(y)2135 1858 y Fu(\007)p Ft(1)2131 1923 y Fv(m)2256 1899 y Fy(=)28 b(1)p Fw(;)216 b Fy(1)27 b Fx(\024)h Fw(m;)17 b(h)28 b Fx(\024)g Fw(s;)-3404 b Fy(\(4.9\))1192 2067 y Fw(y)1240 2082 y Fv(h)1284 2067 y Fw(a)1335 2082 y Fv(j)1400 2067 y Fy(=)27 b Fw(\037)1564 2082 y Fv(j)1601 2067 y Fy(\()p Fw(Y)1696 2082 y Fv(h)1740 2067 y Fy(\))p Fw(a)1829 2082 y Fv(j)1866 2067 y Fw(y)1914 2082 y Fv(h)1958 2067 y Fw(;)216 b Fy(1)28 b Fx(\024)g Fw(h)g Fx(\024)g Fw(s;)33 b Fy(1)28 b Fx(\024)g Fw(j)33 b Fx(\024)c Fw(\022)s(;)-3294 b Fy(\(4.10\))823 2236 y(\(ad)17 b Fw(a)1032 2251 y Fv(i)1060 2236 y Fy(\))1098 2195 y Ft(1)p Fu(\000)p Fv(a)1225 2205 y Fl(ij)1284 2236 y Fw(a)1335 2251 y Fv(j)1400 2236 y Fy(=)27 b(0)p Fw(;)216 b Fy(1)28 b Fx(\024)g Fw(i)g Fx(6)p Fy(=)f Fw(j)34 b Fx(\024)28 b Fw(\022)s(;)117 b(i)27 b Fx(\030)i Fw(j;)-2925 b Fy(\(4.11\))668 2404 y Fw(a)719 2419 y Fv(i)747 2404 y Fw(a)798 2419 y Fv(j)857 2404 y Fx(\000)23 b Fw(\037)1018 2419 y Fv(j)1054 2404 y Fy(\()p Fw(g)1139 2419 y Fv(i)1167 2404 y Fy(\))p Fw(a)1256 2419 y Fv(j)1293 2404 y Fw(a)1344 2419 y Fv(i)1400 2404 y Fy(=)k Fw(\025)1560 2419 y Fv(ij)1621 2404 y Fy(\(1)22 b Fx(\000)g Fw(g)1876 2419 y Fv(i)1904 2404 y Fw(g)1951 2419 y Fv(j)1987 2404 y Fy(\))p Fw(;)216 b Fy(1)28 b Fx(\024)g Fw(i)g(<)f(j)34 b Fx(\024)28 b Fw(\022)s(;)117 b(i)28 b Fx(6\030)g Fw(j)6 b Fy(;)-3404 b(\(4.12\))-180 2600 y Fs(then)35 b Fw(U)10 b Fy(\()p Fx(D)s Fy(\))35 b Fs(is)f(a)h(p)-5 b(ointe)g(d)34 b(Hopf)h(algebr)-5 b(a)34 b(with)h(structur)-5 b(e)36 b(determine)-5 b(d)34 b(by)-180 2796 y Fy(\(4.13\))408 b(\001)p Fw(y)607 2811 y Fv(h)680 2796 y Fy(=)27 b Fw(y)831 2811 y Fv(h)898 2796 y Fx(\012)22 b Fw(y)1045 2811 y Fv(h)1090 2796 y Fw(;)216 b Fy(\001)p Fw(a)1465 2811 y Fv(i)1521 2796 y Fy(=)28 b Fw(a)1676 2811 y Fv(i)1726 2796 y Fx(\012)23 b Fy(1)f(+)g Fw(g)2042 2811 y Fv(i)2092 2796 y Fx(\012)g Fw(a)2242 2811 y Fv(i)2271 2796 y Fw(;)216 b Fy(1)27 b Fx(\024)h Fw(h)g Fx(\024)g Fw(s;)34 b Fy(1)27 b Fx(\024)h Fw(i)g Fx(\024)g Fw(\022)s(:)-80 2992 y Fs(F)-7 b(urthermor)i(e,)36 b Fw(U)10 b Fy(\()p Fx(D)s Fy(\))37 b Fs(has)f(a)g(PBW-b)-5 b(asis)36 b(given)g(by)h(monomials)e(in)i(the)f(r)-5 b(o)g(ot)37 b(ve)-5 b(ctors)37 b Fw(b)3285 3007 y Ft(1)3356 2992 y Fy(:=)31 b Fw(a)3541 3007 y Fv(\014)3581 3016 y Fk(1)3619 2992 y Fw(;)17 b(:)g(:)g(:)f(;)h(b)3879 3007 y Fv(P)3969 2992 y Fy(:=)-180 3132 y Fw(a)-129 3147 y Fv(\014)-89 3158 y Fl(P)-34 3132 y Fs(.)45 b(The)34 b(c)-5 b(or)g(adic)g(al)34 b(\014ltr)-5 b(ation)34 b(of)h Fw(U)10 b Fy(\()p Fx(D)s Fy(\))35 b Fs(is)g(given)f(by)-180 3328 y Fy(\(4.14\))695 b Fw(U)10 b Fy(\()p Fx(D)s Fy(\))997 3343 y Fv(N)1092 3328 y Fy(=)63 b Fs(sp)-5 b(an)34 b(of)h Fw(a)1621 3343 y Fv(i)1645 3352 y Fk(1)1684 3328 y Fw(a)1735 3343 y Fv(i)1759 3352 y Fk(2)1814 3328 y Fw(:)17 b(:)g(:)f(a)1996 3343 y Fv(i)2020 3351 y Fl(s)2058 3328 y Fw(y)31 b Fy(:)127 b Fw(s)28 b Fx(\024)g Fo(N)9 b Fw(;)122 b(y)31 b Fx(2)d Fw(G)p Fy(\()p Fw(H)8 b Fy(\))p Fw(:)-180 3524 y Fs(Ther)-5 b(e)40 b(is)g(an)g(isomorphism)f(of)h(gr)-5 b(ade)g(d)39 b(Hopf)i(algebr)-5 b(as)39 b Fw( )j Fy(:)c Fj(B)p Fy(\()p Fw(V)22 b Fy(\)#)p Fo(|)-9 b Fy(\000)32 b Fx(!)38 b Fy(gr)16 b Fw(U)10 b Fy(\()p Fx(D)s Fy(\))p Fs(,)41 b(given)f(by)h Fw(x)3629 3539 y Fv(i)3657 3524 y Fy(#1)d Fx(7!)p 3963 3469 80 4 v 38 w Fw(a)4014 3539 y Fv(i)4042 3524 y Fs(,)-180 3663 y Fy(1)27 b Fx(\024)i Fw(i)f Fx(\024)g Fw(\022)s Fs(,)35 b Fy(1#)p Fw(Y)468 3678 y Fv(h)540 3663 y Fx(7!)27 b Fw(y)715 3678 y Fv(h)759 3663 y Fs(,)35 b Fy(1)28 b Fx(\024)g Fw(h)g Fx(\024)g Fw(s)p Fs(.)-80 3802 y Fw(U)10 b Fy(\()p Fx(D)s Fy(\))35 b Fs(has)f(\014nite)h(Gelfand-Kiril)5 b(lov)33 b(dimension)g(and)h(is)h(a)g(domain.)-80 3947 y Fy(In)43 b(\(4.12\))g(and)g(\(4.13\))o(,)j(the)e(elemen)m(ts)g Fw(g)1503 3962 y Fv(i)1530 3947 y Fy(,)i(1)g Fx(\024)g Fw(i)h Fx(\024)f Fw(\022)s Fy(,)g(m)m(ust)d(b)s(e)h(read)f(as)h(the)f (w)m(ord)h(in)f(the)g(generators)-180 4075 y Fw(y)-132 4090 y Fv(h)-88 4075 y Fw(;)17 b Fy(1)28 b Fx(\024)g Fw(h)g Fx(\024)g Fw(s)k Fy(giv)m(en)h(b)m(y)g Fw(y)847 4021 y Fv(t)872 4031 y Fl(i;)p Fk(1)843 4100 y Ft(1)968 4075 y Fx(\001)17 b(\001)g(\001)e Fw(y)1153 4021 y Fv(t)1178 4031 y Fl(i;s)1149 4085 y Fv(s)1256 4075 y Fy(,)33 b(if)e Fw(g)1452 4090 y Fv(i)1508 4075 y Fy(=)d Fw(Y)1690 4021 y Fv(t)1715 4031 y Fl(i;)p Fk(1)1669 4100 y Ft(1)1812 4075 y Fx(\001)17 b(\001)g(\001)e Fw(Y)2023 4021 y Fv(t)2048 4031 y Fl(i;s)2002 4085 y Fv(s)2127 4075 y Fy(,)32 b(where)i Fw(t)2503 4090 y Fv(i;)p Ft(1)2587 4075 y Fw(;)17 b Fx(\001)g(\001)g (\001)31 b Fw(;)17 b(t)2859 4090 y Fv(i;s)2972 4075 y Fy(are)32 b(natural)g(n)m(um)m(b)s(ers.)-80 4191 y(The)37 b(relations)f(\(4.11\))g(are)h(the)g(quan)m(tum)g(Serre)g(relations.)55 b(By)39 b(\(4.10\))d(and)h(\(4.13\))o(,)h(\(ad)16 b Fw(a)3427 4206 y Fv(i)3455 4191 y Fy(\)\()p Fw(a)3582 4206 y Fv(j)3619 4191 y Fy(\))35 b(=)f Fw(a)3853 4206 y Fv(i)3882 4191 y Fw(a)3933 4206 y Fv(j)3994 4191 y Fx(\000)-180 4308 y Fw(\037)-119 4323 y Fv(j)-82 4308 y Fy(\()p Fw(g)3 4323 y Fv(i)30 4308 y Fy(\))p Fw(a)119 4323 y Fv(j)156 4308 y Fw(a)207 4323 y Fv(i)263 4308 y Fy(=)28 b(\(ad)524 4323 y Fv(c)559 4308 y Fw(a)610 4323 y Fv(i)638 4308 y Fy(\)\()p Fw(a)765 4323 y Fv(j)802 4308 y Fy(\).)43 b(Here,)33 b(ad)1286 4323 y Fv(c)1354 4308 y Fy(is)f(the)g(braided)h (adjoin)m(t)e(represen)m(tation)i(in)f(the)h(tensor)g(algebra)e(of)h Fw(V)22 b Fy(.)-180 4424 y(Hence)34 b(the)f(left)f(hand)g(side)h(of)39 b(\(4.11\))32 b(should)g(b)s(e)h(more)f(formally)e(written)i(as)663 4702 y(\(ad)820 4717 y Fv(c)855 4702 y Fw(a)906 4717 y Fv(i)934 4702 y Fy(\))972 4661 y Ft(1)p Fu(\000)p Fv(aij)1161 4702 y Fy(\()p Fw(a)1250 4717 y Fv(j)1286 4702 y Fy(\))c(=)1455 4566 y Ft(1)p Fu(\000)p Fv(a)1582 4576 y Fl(ij)1475 4607 y Fn(X)1491 4819 y Fv(l)q Ft(=0)1638 4702 y Fy(\()p Fx(\000)p Fy(1\))1840 4661 y Fv(l)1866 4561 y Fn(\022)1939 4634 y Fy(1)22 b Fx(\000)h Fw(a)2161 4649 y Fv(ij)2065 4770 y Fw(l)2222 4561 y Fn(\023)2295 4801 y Fv(q)2327 4811 y Fl(ii)2379 4702 y Fw(q)2436 4608 y Fl(l)p Fk(\()p Fl(l)p Fg(\000)p Fk(1\))p 2436 4626 167 3 v 2504 4667 a(2)2422 4727 y Fv(ii)2616 4702 y Fw(q)2663 4661 y Fv(l)2659 4726 y(ij)2720 4702 y Fw(a)2771 4648 y Ft(1)p Fu(\000)p Fv(a)2898 4658 y Fl(ij)2954 4648 y Fu(\000)p Fv(l)2771 4727 y(i)3035 4702 y Fw(a)3086 4717 y Fv(j)3122 4702 y Fw(a)3173 4661 y Fv(l)3173 4726 y(i)3202 4702 y Fw(;)-180 4969 y Fy(where)34 b Fw(q)145 4984 y Fv(ij)233 4969 y Fy(:=)28 b Fw(\037)425 4984 y Fv(j)462 4969 y Fy(\()p Fw(g)547 4984 y Fv(i)574 4969 y Fy(\))33 b(for)f(all)e Fw(i;)17 b(j)6 b Fy(.)-180 5177 y Fs(Pr)-5 b(o)g(of.)41 b(Step)36 b(I)p Fy(.)d(It)g(is)g(not)h (di\016cult)e(to)h(see)i(that)e(\001)h(is)f(w)m(ell-de\014ned)h(b)m(y)i (\(4.13\))o(,)e(using)f(Lemma)f(2.1)h(\(b\))h(for)e(the)-180 5317 y(quan)m(tum)h(Serre)g(relations.)p eop %%Page: 15 15 15 14 bop 1010 0 a Fp(A)33 b(CHARA)n(CTERIZA)-6 b(TION)31 b(OF)i(QUANTUM)f(GR)n(OUPS)1112 b(15)-80 203 y Fs(Step)39 b(II)p Fy(.)d(As)j(in)d([AS4,)j(Th.)59 b(4.5],)39 b(w)m(e)f(deduce)h (from)e(Theorem)g(2.10,)i(via)d(Prop)s(osition)g(2.2,)j(that)e Fj(B)p Fy(\()p Fw(V)21 b Fy(\))36 b Fx(')-180 342 y Fo(|)-9 b Fx(h)p Fw(x)-25 357 y Ft(1)9 342 y Fw(;)17 b(:)g(:)g(:)f(;)h(x)283 357 y Fv(\022)322 342 y Fx(j)p Fy(ad)469 357 y Fv(c)504 342 y Fy(\()p Fw(x)597 357 y Fv(i)625 342 y Fy(\))663 306 y Ft(1)p Fu(\000)p Fv(a)790 316 y Fl(ij)877 342 y Fy(=)28 b(0)p Fw(;)17 b Fy(1)27 b Fx(\024)h Fw(i)g Fx(6)p Fy(=)f Fw(j)34 b Fx(\024)28 b Fw(\022)s Fx(i)p Fy(.)-80 553 y Fs(Step)35 b(III)p Fy(.)d(W)-8 b(e)33 b(no)m(w)h(pro)m(v)m(e)g (the)g(statemen)m(t)g(ab)s(out)e(the)i(PBW-basis.)45 b(W)-8 b(e)34 b(argue)f(exactly)h(as)f(in)f(the)i(pro)s(of)e(of)-180 693 y([AS4,)38 b(Th.)57 b(5.17];)38 b(w)m(e)g(pro)s(ceed)f(b)m(y)h (induction)e(on)h(the)g(n)m(um)m(b)s(er)g(of)f(connected)j(comp)s(onen) m(ts.)56 b(If)37 b(the)g(Dynkin)-180 832 y(diagram)h(is)h(connected,)44 b(the)c(claim)e(follo)m(ws)h(from)f(Step)j(I)s(I)f(as)g(in)f([AS4,)j (Lemma)d(5.18].)65 b(F)-8 b(or)39 b(the)i(inductiv)m(e)-180 972 y(step,)47 b(one)c(rep)s(eats)h(the)f(argumen)m(t)g(in)f([AS4,)k (Lemma)41 b(5.19].)74 b(W)-8 b(e)44 b(assume)f(there)h(exists)3361 945 y Fn(b)3357 972 y Fw(\022)k(<)e(\022)g Fy(suc)m(h)e(that)-180 1111 y Fw(J)c Fy(=)31 b Fx(f)p Fy(1)p Fw(;)17 b(:)g(:)g(:)f(;)343 1085 y Fn(b)339 1111 y Fw(\022)s Fx(g)31 b(2)g(X)15 b Fy(.)50 b(Let)35 b(\007)c(:=)p Fw(<)g(Z)1289 1126 y Ft(1)1359 1111 y Fw(>)g Fx(\010)17 b(\001)g(\001)g(\001)e(\010)32 b Fw(<)f(Z)1980 1125 y Fm(b)1976 1142 y Fv(\022)2046 1111 y Fw(>)p Fy(,)k(b)s(e)g(a)f(free)h(ab)s(elian)e(group)i(of)f(rank) 3555 1085 y Fn(b)3551 1111 y Fw(\022)s Fy(.)50 b(Let)34 b Fw(\021)3900 1126 y Fv(j)3972 1111 y Fy(b)s(e)-180 1251 y(the)f(unique)g(c)m(haracter)g(of)g(\007)f(suc)m(h)i(that)e Fw(\021)1429 1266 y Fv(j)1466 1251 y Fy(\()p Fw(Z)1571 1266 y Fv(i)1599 1251 y Fy(\))27 b(=)h Fw(\037)1829 1266 y Fv(j)1866 1251 y Fy(\()p Fw(g)1951 1266 y Fv(i)1978 1251 y Fy(\),)33 b(1)27 b Fx(\024)i Fw(i;)17 b(j)33 b Fx(\024)2518 1224 y Fn(b)2513 1251 y Fw(\022)t Fy(.)-80 1390 y(Let)f Fx(D)171 1405 y Ft(1)242 1390 y Fy(b)s(e)g(the)g(generic)g (datum)f(o)m(v)m(er)i(\000)e(giv)m(en)h(b)m(y)h(\()p Fw(a)1957 1405 y Fv(ij)2018 1390 y Fy(\))2060 1404 y Fm(b)2056 1421 y Fv(\022)r()c(l)-180 409 y Fy(\(4.15\))1016 b Fw(b)1127 424 y Fv(k)1170 409 y Fw(b)1211 424 y Fv(l)1260 409 y Fx(\000)23 b Fw(\037)1421 424 y Fv(\014)1461 436 y Fl(l)1489 409 y Fy(\()p Fw(g)1574 424 y Fv(\014)1614 436 y Fl(k)1655 409 y Fy(\))p Fw(b)1734 424 y Fv(l)1761 409 y Fw(b)1802 424 y Fv(k)1872 409 y Fy(=)1995 314 y Fn(X)1976 533 y Ff(c)p Fu(2)p Fh(N)2103 514 y Fl(P)2175 409 y Fw(\032)2225 424 y Ff(c)2282 409 y Fw(b)2323 365 y Fv(c)2354 374 y Fk(1)2323 433 y Ft(1)2393 409 y Fw(b)2434 365 y Fv(c)2465 374 y Fk(2)2434 433 y Ft(2)2520 409 y Fw(:)17 b(:)g(:)f(b)2692 363 y Fv(c)2723 374 y Fl(P)2692 436 y Fv(P)2779 409 y Fw(;)-180 697 y Fy(where)34 b Fw(\032)152 712 y Ff(c)220 697 y Fx(2)28 b Fo(|)-8 b Fy(,)26 b(and)33 b Fw(\032)669 712 y Ff(c)737 697 y Fy(=)28 b(0)k(unless)h(deg)19 b(\()p Fw(b)1454 653 y Fv(c)1485 662 y Fk(1)1454 721 y Ft(1)1523 697 y Fw(b)1564 653 y Fv(c)1595 662 y Fk(2)1564 721 y Ft(2)1651 697 y Fw(:)e(:)g(:)f(b)1823 651 y Fv(c)1854 662 y Fl(P)1823 724 y Fv(P)1909 697 y Fy(\))28 b Fw(<)f Fy(deg)18 b(\()p Fw(b)2321 712 y Fv(l)2348 697 y Fw(b)2389 712 y Fv(k)2432 697 y Fy(\).)-80 836 y(If)31 b Fw(\014)71 851 y Fv(l)128 836 y Fy(and)h Fw(\014)372 851 y Fv(k)446 836 y Fy(ha)m(v)m(e)g(supp)s(ort)g(in)f(the)g(same)h(connected)h(comp)s (onen)m(t,)e(then)h(\(4.15\))f(follo)m(ws)f(from)g(the)i(form)m(ula) -180 976 y(of)37 b(Lev)m(endorskii)h(and)f(Soib)s(elman)e([DCK,)k (Lemma)d(1.7])h(using)g(Lemma)f(2.2.)58 b(Note)37 b(that)g(here)h(w)m (e)h(are)e(using)-180 1115 y(the)31 b(sp)s(ecial)f(order)i(of)e(the)i (set)f(of)g(p)s(ositiv)m(e)f(ro)s(ots,)h(in)f(whic)m(h)i(the)f(ro)s (ots)g(with)g(supp)s(ort)g(on)g(the)g(\014rst)h(comp)s(onen)m(t)-180 1255 y(are)h(smaller)d(than)j(the)g(ro)s(ots)f(in)g(the)h(second,)h (and)e(so)h(on.)-80 1394 y(If)f Fw(\014)72 1409 y Fv(l)131 1394 y Fy(and)h Fw(\014)376 1409 y Fv(k)452 1394 y Fy(ha)m(v)m(e)h (supp)s(ort)f(in)g(di\013eren)m(t)g(connected)h(comp)s(onen)m(ts,)g (then)f(\(4.15\))f(follo)m(ws)g(from)g(the)h(linking)-180 1534 y(relations)e(since)i(the)g(monomials)c(in)j(an)m(y)i(ro)s(ot)d(v) m(ector)j(are)e(homogeneous.)-80 1673 y(As)e(in)e([DCK,)i(Corollary)e (1.8],)h(it)g(is)f(not)i(di\016cult)e(to)h(v)m(erify)h(that)f(the)h (asso)s(ciated)f(graded)g(ring)g(is)f(a)i(domain,)-180 1813 y(whic)m(h)j(implies)d(that)j Fw(U)10 b Fy(\()p Fx(D)s Fy(\))32 b(is)g(a)h(domain.)2565 b Fi(\003)-80 2010 y Fy(T)-8 b(o)26 b(describ)s(e)g(the)h(isomorphisms)d(b)s(et)m(w)m (een)k(Hopf)e(algebras)f Fw(U)10 b Fy(\()p Fx(D)s Fy(\))26 b(and)h Fw(U)10 b Fy(\()p Fx(D)2802 1974 y Fu(0)2825 2010 y Fy(\),)27 b(w)m(e)h(\014rst)e(form)m(ulate)f(a)g(Lemma)-180 2126 y(whic)m(h)33 b(is)f(needed)i(in)e(this)g(general)g(form)g(in)g (the)h(pro)s(of)e(of)h(the)h(main)e(theorem)i(5.2.)-180 2299 y FC(Lemma)46 b(4.3.)f Fs(L)-5 b(et)43 b Fy(\000)e Fs(b)-5 b(e)42 b(a)f(\014nitely)h(gener)-5 b(ate)g(d)41 b(ab)-5 b(elian)41 b(gr)-5 b(oup,)43 b Fw(A)f Fs(a)g(p)-5 b(ointe)g(d)41 b(Hopf)h(algebr)-5 b(a)40 b(with)i(c)-5 b(or)g(adic)g(al)-180 2438 y Fw(A)-107 2453 y Ft(0)-40 2438 y Fy(=)28 b Fo(|)-9 b Fy(\000)p Fs(,)29 b Fw(V)49 b Fx(2)445 2402 y Fh(|)-14 b Ft(\000)445 2464 y Fh(|)g Ft(\000)530 2438 y Fx(Y)8 b(D)38 b Fs(with)c Fo(|)-8 b Fs(-)o(b)j(asis)29 b Fw(x)1311 2453 y Fv(i)1367 2438 y Fx(2)f Fw(V)1540 2402 y Fv(\037)1584 2412 y Fl(i)1518 2463 y Fv(g)1552 2473 y Fl(i)1614 2438 y Fw(;)17 b(g)1705 2453 y Fv(i)1760 2438 y Fx(2)28 b Fy(\000)p Fw(;)17 b(\037)2020 2453 y Fv(i)2076 2438 y Fx(2)2173 2413 y Fn(b)2170 2438 y Fy(\000)p Fw(;)g Fy(1)27 b Fx(\024)h Fw(i)g Fx(\024)g Fw(\022)s(:)-80 2578 y Fs(Assume)34 b(that)i(gr)p Fw(A)669 2550 y Fx(\030)670 2582 y Fy(=)775 2578 y Fj(B)p Fy(\()p Fw(V)21 b Fy(\)#)p Fo(|)-8 b Fy(\000)29 b Fs(as)34 b(gr)-5 b(ade)g(d)34 b(Hopf)h(algebr)-5 b(as,)34 b(and)-180 2784 y Fy(\(4.16\))1345 b Fw(\037)1476 2799 y Fv(i)1532 2784 y Fx(6)p Fy(=)27 b Fw(";)51 b Fs(for)35 b(al)5 b(l)34 b Fy(1)28 b Fx(\024)g Fw(i)g Fx(\024)g Fw(\022)s(:)-180 2990 y Fs(Then)34 b(the)h(\014rst)g(term)g(of)f(the)h(c)-5 b(or)g(adic)g(al)34 b(\014ltr)-5 b(ation)35 b(of)f Fw(A)h Fs(is)1286 3195 y Fw(A)1359 3210 y Ft(1)1426 3195 y Fy(=)27 b Fw(A)1602 3210 y Ft(0)1664 3195 y Fx(\010)1864 3101 y Fn(M)1764 3313 y Fv(g)r Fu(2)p Ft(\000)p Fv(;)p Ft(1)p Fu(\024)p Fv(i)p Fu(\024)p Fv(\022)2131 3195 y Fx(P)2200 3210 y Fv(g)r(g)2270 3220 y Fl(i)2296 3210 y Fv(;g)2356 3195 y Fy(\()p Fw(A)p Fy(\))2505 3154 y Fv(\037)2549 3164 y Fl(i)2579 3195 y Fw(:)-180 3485 y Fs(If)46 b Fy(\()p Fw(g)19 3500 y Fv(i)46 3485 y Fw(;)17 b(\037)151 3500 y Fv(i)179 3485 y Fy(\))49 b Fx(6)p Fy(=)f(\()p Fw(g)475 3500 y Fv(j)511 3485 y Fw(;)17 b(\037)616 3500 y Fv(j)653 3485 y Fy(\))46 b Fs(for)g(al)5 b(l)45 b Fw(i)k Fx(6)p Fy(=)g Fw(j)6 b Fs(,)48 b(then)e(the)h(ve)-5 b(ctor)45 b(sp)-5 b(ac)g(es)46 b Fx(P)2460 3500 y Fv(g)r(g)2530 3510 y Fl(i)2556 3500 y Fv(;g)2616 3485 y Fy(\()p Fw(A)p Fy(\))2765 3449 y Fv(\037)2809 3459 y Fl(i)2885 3485 y Fs(ar)-5 b(e)46 b(one-dimensional)d(for)j(al)5 b(l)-180 3625 y Fw(g)31 b Fx(2)d Fy(\000)p Fw(;)17 b Fy(1)27 b Fx(\024)h Fw(i)g Fx(\024)g Fw(\022)s Fs(.)-180 3845 y(Pr)-5 b(o)g(of.)41 b Fy(By)e(assumption,)h Fw(A)901 3860 y Ft(1)940 3845 y Fw(=)-5 b(A)1057 3860 y Ft(0)1134 3818 y Fx(\030)1135 3849 y Fy(=)1250 3845 y Fw(V)21 b Fy(#)p Fo(|)-8 b Fy(\000,)34 b(and)39 b(the)g(elemen)m(ts)g Fw(x)2423 3860 y Fv(i)2451 3845 y Fy(#)p Fw(g)j Fx(2)c(P)2794 3860 y Fv(g)r(g)2864 3870 y Fl(i)2891 3860 y Fv(;g)2950 3845 y Fy(\()p Fj(B)p Fy(\()p Fw(V)22 b Fy(\)#)p Fo(|)-9 b Fy(\000\))3472 3809 y Fv(\037)3516 3819 y Fl(i)3541 3845 y Fy(,)40 b(1)e Fx(\024)g Fw(i)g Fx(\024)h Fw(\022)s Fy(,)-180 3985 y Fw(g)31 b Fx(2)d Fy(\000,)33 b Fw(x)28 b Fx(2)g(P)359 4000 y Fv(g)r(g)429 4010 y Fl(i)455 4000 y Fv(;g)515 3985 y Fy(\()p Fw(A)p Fy(\))664 3949 y Fv(\037)708 3959 y Fl(i)771 3985 y Fy(form)j(a)h Fo(|)-8 b Fy(-)o(basis)27 b(of)32 b Fw(V)21 b Fy(#)p Fo(|)-8 b Fy(\000.)37 b(Hence)1420 4192 y Fw(A)1493 4207 y Ft(1)1533 4192 y Fw(=)-5 b(A)1650 4207 y Ft(0)1717 4164 y Fx(\030)1717 4196 y Fy(=)1848 4097 y Fn(M)1822 4309 y Ft(1)p Fu(\024)p Fv(i)p Fu(\024)p Fv(\022)2026 4192 y Fy(\()p Fw(A)2137 4207 y Ft(1)2176 4192 y Fw(=)g(A)2293 4207 y Ft(0)2332 4192 y Fy(\))2370 4151 y Fv(\037)2414 4161 y Fl(i)2444 4192 y Fw(:)-180 4480 y Fy(Let)39 b Fw(h)57 4495 y Ft(1)96 4480 y Fw(;)17 b Fx(\001)g(\001)g(\001)32 b Fw(;)17 b(h)390 4495 y Fv(s)465 4480 y Fy(b)s(e)39 b(generators)g(of)f(\000.)62 b(Fix)38 b(1)f Fx(\024)i Fw(i)f Fx(\024)h Fw(\022)s Fy(.)62 b(Then)40 b(for)e(an)m(y)h Fw(a)f Fx(2)h Fw(A)2929 4495 y Ft(1)3007 4480 y Fy(with)g(\026)-50 b Fw(a)38 b Fx(2)h Fy(\()p Fw(A)3540 4495 y Ft(1)3579 4480 y Fw(=)-5 b(A)3696 4495 y Ft(0)3735 4480 y Fy(\))3773 4444 y Fv(\037)3817 4454 y Fl(i)3848 4480 y Fy(,)40 b(and)-180 4619 y(1)32 b Fx(\024)h Fw(l)i Fx(\024)e Fw(s)p Fy(,)k(the)f(adjoin)m(t)e(action)h(of)g Fw(h)1265 4634 y Fv(l)1326 4619 y Fy(on)h Fw(a)f Fy(is)g(giv)m(en)h(b)m (y)g Fw(h)2104 4634 y Fv(l)2154 4619 y Fx(\001)24 b Fw(a)33 b Fy(=)g Fw(\037)2460 4634 y Fv(i)2488 4619 y Fy(\()p Fw(h)2582 4634 y Fv(l)2608 4619 y Fy(\))p Fw(a)24 b Fy(+)g Fw(v)2868 4634 y Fv(l)2894 4619 y Fy(,)37 b(for)e(some)g Fw(v)3404 4634 y Fv(l)3463 4619 y Fx(2)e Fw(A)3635 4634 y Ft(0)3674 4619 y Fy(.)52 b(Since)36 b(\000)-180 4759 y(is)d(ab)s(elian,)g(the)h(v)m(ector)h(space)g(spanned)g(b)m(y)f Fw(a;)17 b(v)1671 4774 y Ft(1)1711 4759 y Fw(;)g Fx(\001)g(\001)g(\001) 31 b Fw(;)17 b(v)1995 4774 y Fv(s)2065 4759 y Fy(is)34 b(\000-stable)f(con)m(taining)f Fw(a)p Fy(.)47 b(This)34 b(sho)m(ws)i(that)d Fw(A)3933 4774 y Ft(1)4006 4759 y Fy(is)-180 4898 y(lo)s(cally)f(\014nite)j(under)g(the)h(adjoin)m(t)e (action)g(of)g(\000.)50 b(W)-8 b(e)36 b(claim)c(that)j Fw(A)2431 4913 y Ft(1)2505 4898 y Fy(is)f(completely)g(reducible)h(as)g (\000-mo)s(dule.)-180 5038 y(Indeed,)48 b(let)43 b Fw(U)55 b Fy(b)s(e)44 b(an)m(y)g(lo)s(cally)d(\014nite)j(\000-mo)s(dule,)g(let) f Fw(\037)k Fx(2)2225 5013 y Fn(b)2222 5038 y Fy(\000,)g(and)d(let)f Fw(U)2786 5002 y Ft(\()p Fv(\037)p Ft(\))2936 5038 y Fy(=)k Fx(f)p Fw(u)f Fx(2)h Fw(U)57 b Fy(:)47 b Fx(9)p Fw(s)g(>)g Fy(0)c(suc)m(h)-180 5177 y(that)f(\()p Fw(g)32 b Fx(\000)e Fw(\037)p Fy(\()p Fw(g)t Fy(\)\))491 5141 y Fv(s)527 5177 y Fy(\()p Fw(u)p Fy(\))44 b(=)g(0)p Fx(8)p Fw(g)k Fx(2)d Fy(\000)p Fx(g)p Fy(.)73 b(Then)43 b Fw(U)55 b Fy(=)45 b Fx(\010)1927 5208 y Fv(\037)p Fu(2)2020 5191 y Fm(b)2018 5208 y Ft(\000)2066 5177 y Fw(U)2142 5141 y Ft(\()p Fv(\037)p Ft(\))2288 5177 y Fy(\(see)f(for)e(instance)g([D,)j (Th.)74 b(1.3.19]\).)e(No)m(w,)-180 5317 y Fw(A)-107 5332 y Ft(0)-40 5317 y Fx(\032)28 b Fy(\()p Fw(A)176 5332 y Ft(1)216 5317 y Fy(\))254 5281 y Fv(")318 5317 y Fx(\032)g Fy(\()p Fw(A)534 5332 y Ft(1)574 5317 y Fy(\))612 5281 y Ft(\()p Fv(")p Ft(\))703 5317 y Fy(,)33 b(but)g(b)m(y)i (\(4.16\))o(,)e(they)g(are)g(all)d(three)k(equal.)43 b(The)33 b(claim)e(follo)m(ws.)p eop %%Page: 17 17 17 16 bop 1010 0 a Fp(A)33 b(CHARA)n(CTERIZA)-6 b(TION)31 b(OF)i(QUANTUM)f(GR)n(OUPS)1112 b(17)-80 203 y Fy(Hence)38 b Fw(A)287 218 y Ft(1)363 203 y Fy(=)d Fw(A)547 218 y Ft(0)612 203 y Fx(\010)715 128 y Fn(L)826 232 y Ft(1)p Fu(\024)p Fv(i)p Fu(\024)p Fv(\022)1034 203 y Fy(\()p Fw(A)1145 218 y Ft(1)1184 203 y Fy(\))1222 167 y Fv(\037)1266 177 y Fl(i)1297 203 y Fy(.)57 b(By)38 b(the)g(theorem)f(of)g(T)-8 b(aft)37 b(and)h(Wilson)e([M,)j(Theorem)f(5.4.1],)g Fw(A)3921 218 y Ft(1)3996 203 y Fy(=)-180 342 y Fw(A)-107 357 y Ft(0)-45 342 y Fy(+)22 b(\()91 268 y Fn(L)201 372 y Fv(g)r(;h)p Fu(2)p Ft(\000)409 342 y Fx(P)478 357 y Fv(g)r(;h)579 342 y Fy(\()p Fw(A)p Fy(\)\).)44 b(Hence)1287 566 y Fw(A)1360 581 y Ft(1)1427 566 y Fy(=)28 b Fw(A)1604 581 y Ft(0)1666 566 y Fx(\010)1905 471 y Fn(M)1765 702 y Fv(g)r(;h)p Fu(2)p Ft(\000)p Fv(;")p Fu(6)p Ft(=)p Fv(\037)p Fu(2)2154 685 y Fm(b)2152 702 y Ft(\000)2211 566 y Fx(P)2280 581 y Fv(g)r(;h)2381 566 y Fy(\()p Fw(A)p Fy(\))2530 524 y Fv(\037)2578 566 y Fw(;)-180 870 y Fy(and)33 b(the)g(lemma)d(follo)m (ws.)3186 b Fi(\003)-80 1070 y Fy(Note)32 b(that)h(\(4.16\))f(holds)g (for)g(generic)g(braidings,)g(since)h(in)f(this)g(case)h(no)g Fw(\037)2780 1085 y Fv(i)2808 1070 y Fy(\()p Fw(g)2893 1085 y Fv(i)2921 1070 y Fy(\))f(is)g(a)h(ro)s(ot)e(of)h(1.)-80 1186 y(If)40 b Fw(A;)17 b(B)44 b Fy(are)c(Hopf)g(algebras,)i(w)m(e)f (denote)f(the)h(set)f(of)g(all)e(Hopf)i(algebra)e(isomorphisms)h(from)f Fw(A)i Fy(to)g Fw(B)45 b Fy(b)m(y)-180 1303 y(Isom\()p Fw(A;)17 b(B)5 b Fy(\).)-180 1476 y FC(Theorem)43 b(4.4.)h Fs(L)-5 b(et)40 b Fx(D)j Fs(and)c Fx(D)1086 1440 y Fu(0)1148 1476 y Fs(b)-5 b(e)39 b(generic)g(data)g(of)h(\014nite)f(Cartan)g(typ) -5 b(e)40 b(for)f Fy(\000)p Fs(.)59 b(Then)39 b(the)g(Hopf)h(algebr)-5 b(as)-180 1616 y Fw(U)10 b Fy(\()p Fx(D)s Fy(\))35 b Fs(and)f Fw(U)10 b Fy(\()p Fx(D)470 1580 y Fu(0)494 1616 y Fy(\))35 b Fs(ar)-5 b(e)34 b(isomorphic)g(if)g(and)h(only)f(if)h Fx(D)i Fs(is)e(isomorphic)e(to)i Fx(D)2737 1580 y Fu(0)2760 1616 y Fs(.)-80 1755 y(Mor)-5 b(e)39 b(pr)-5 b(e)g(cisely,)39 b(let)g Fw(a)796 1770 y Ft(1)835 1755 y Fw(;)17 b Fx(\001)g(\001)g (\001)32 b Fw(;)17 b(a)1124 1770 y Fv(\022)1201 1755 y Fs(r)-5 b(esp.)57 b Fw(a)1510 1719 y Fu(0)1510 1780 y Ft(1)1549 1755 y Fw(;)17 b Fx(\001)g(\001)g(\001)31 b Fw(;)17 b(a)1837 1719 y Fu(0)1837 1781 y Fv(\022)1915 1755 y Fs(b)-5 b(e)39 b(the)g(simple)f(r)-5 b(o)g(ot)39 b(ve)-5 b(ctors)38 b(in)h Fw(U)10 b Fy(\()p Fx(D)s Fy(\))39 b Fs(r)-5 b(esp.)56 b Fw(U)10 b Fy(\()p Fx(D)3892 1719 y Fu(0)3915 1755 y Fy(\))39 b Fs(of)-180 1895 y(The)-5 b(or)g(em)33 b(4.2,)h(and)g(let)g Fw(g)790 1910 y Ft(1)829 1895 y Fw(;)17 b Fx(\001)g(\001)g(\001)31 b Fw(;)17 b(g)1113 1910 y Fv(\022)1186 1895 y Fs(r)-5 b(esp.)44 b Fw(g)1482 1859 y Fu(0)1478 1919 y Ft(1)1517 1895 y Fw(;)17 b Fx(\001)g(\001)g (\001)32 b Fw(;)17 b(g)1806 1859 y Fu(0)1802 1921 y Fv(\022)1874 1895 y Fs(b)-5 b(e)34 b(the)h(gr)-5 b(oup-like)33 b(elements)h(in)g Fx(D)j Fs(r)-5 b(esp.)44 b Fx(D)3560 1859 y Fu(0)3617 1895 y Fs(.)g(Then)34 b(the)-180 2034 y(map)1193 2201 y(Isom)o Fy(\()p Fw(U)10 b Fy(\()p Fx(D)s Fy(\))p Fw(;)17 b(U)10 b Fy(\()p Fx(D)1908 2160 y Fu(0)1932 2201 y Fy(\)\))27 b Fx(!)g Fs(Isom)o Fy(\()p Fx(D)s Fw(;)17 b Fx(D)2611 2160 y Fu(0)2634 2201 y Fy(\))p Fw(;)-180 2389 y Fs(given)32 b(by)g Fw(\036)c Fx(7!)f Fy(\()p Fw(';)17 b(\033)n(;)g Fy(\()p Fw(\013)752 2404 y Fv(i)780 2389 y Fy(\)\))p Fs(,)33 b(wher)-5 b(e)31 b Fw(')p Fy(\()p Fw(g)t Fy(\))c(=)h Fw(\036)p Fy(\()p Fw(g)t Fy(\))p Fw(;)17 b(')p Fy(\()p Fw(g)1891 2404 y Fv(i)1917 2389 y Fy(\))28 b(=)f Fw(g)2137 2352 y Fu(0)2133 2418 y Fv(\033)r Ft(\()p Fv(i)p Ft(\))2259 2389 y Fw(;)17 b(\036)p Fy(\()p Fw(a)2450 2404 y Fv(i)2477 2389 y Fy(\))28 b(=)g Fw(\013)2709 2404 y Fv(i)2737 2389 y Fw(a)2788 2352 y Fu(0)2788 2418 y Fv(\033)r Ft(\()p Fv(i)p Ft(\))2914 2389 y Fs(,)33 b(for)f(al)5 b(l)32 b Fw(g)f Fx(2)d Fy(\000)p Fw(;)17 b Fy(1)27 b Fx(\024)h Fw(i)g Fx(\024)g Fw(\022)s Fs(,)33 b(is)-180 2528 y(bije)-5 b(ctive.)-180 2751 y(Pr)g(o)g(of.)41 b Fy(Let)h Fw(V)64 b Fy(resp.)73 b Fw(V)774 2715 y Fu(0)839 2751 y Fy(b)s(e)43 b(the)f(Y)-8 b(etter-Drinfeld)40 b(mo)s(dule)h(of)g(the)i (in\014nitesimal)38 b(braiding)j(of)g Fw(A)j Fy(:=)g Fw(U)10 b Fy(\()p Fx(D)s Fy(\))-180 2891 y(resp.)86 b(of)45 b Fw(A)303 2854 y Fu(0)378 2891 y Fy(:=)51 b Fw(U)10 b Fy(\()p Fx(D)s Fy(\).)85 b(Let)46 b Fw(\036)51 b Fy(:)g Fw(A)h Fx(!)e Fw(A)1599 2854 y Fu(0)1669 2891 y Fy(b)s(e)c(an)h (isomorphism)d(of)h(Hopf)i(algebras.)84 b(Then)47 b Fw(\036)f Fy(induces)-180 3030 y(isomorphisms)28 b Fw(A)499 3045 y Ft(0)566 3030 y Fx(!)g Fw(A)767 2994 y Fu(0)767 3055 y Ft(0)836 3030 y Fy(and)i Fw(A)1096 3045 y Ft(1)1164 3030 y Fx(!)d Fw(A)1364 2994 y Fu(0)1364 3055 y Ft(1)1403 3030 y Fy(.)43 b(Hence)31 b Fw(\036)f Fy(de\014nes)i(an)e(isomorphism)e (of)h(groups)h Fw(')e Fy(:)g(\000)f Fx(!)h Fy(\000,)i(and)g(for)-180 3169 y(all)g Fw(g)t(;)17 b(h)27 b Fx(2)h Fy(\000)p Fw(;)17 b(\037)28 b Fx(2)518 3144 y Fn(b)515 3169 y Fy(\000,)k(a)h(linear)e (isomorphism)1323 3377 y Fx(P)1392 3392 y Fv(g)r(;h)1492 3377 y Fy(\()p Fw(A)p Fy(\))1641 3336 y Fv(\037)1717 3350 y Fx(\030)1718 3381 y Fy(=)1822 3377 y Fx(P)1891 3393 y Fv(')p Ft(\()p Fv(g)r Ft(\))p Fv(;')p Ft(\()p Fv(h)p Ft(\))2193 3377 y Fy(\()p Fw(A)2304 3336 y Fu(0)2328 3377 y Fy(\))2366 3336 y Fv(\037')2456 3313 y Fg(\000)p Fk(1)2542 3377 y Fw(:)-180 3585 y Fy(By)39 b(Theorem)g(4.2,)g(the)g (assumptions)f(of)g(Lemma)g(4.3)g(are)g(satis\014ed)h(for)f Fw(A;)17 b(V)60 b Fy(and)38 b Fw(A)3163 3549 y Fu(0)3187 3585 y Fw(;)17 b(V)3309 3549 y Fu(0)3332 3585 y Fy(.)61 b(Then)40 b(it)d(follo)m(ws)-180 3724 y(from)42 b(Lemma)g(4.3)g(and)h (\(4.8\))g(that)g(there)h(is)e(a)h(uniquely)g(determined)g(p)s(erm)m (utation)f Fw(\033)49 b Fx(2)d Fo(S)3486 3739 y Fv(\022)3562 3724 y Fy(suc)m(h)e(that)f Fw(\036)-180 3864 y Fy(induces)33 b(an)g(isomorphism)266 4072 y Fx(P)335 4087 y Fv(g)369 4097 y Fl(i)395 4087 y Fv(;)p Ft(1)454 4072 y Fy(\()p Fw(A)p Fy(\))603 4030 y Fv(\037)647 4040 y Fl(i)705 4044 y Fx(\030)706 4076 y Fy(=)810 4072 y Fx(P)879 4088 y Fv(g)915 4065 y Fg(0)913 4114 y Fl(\033)r Fk(\()p Fl(i)p Fk(\))1025 4088 y Fv(;)p Ft(1)1084 4072 y Fy(\()p Fw(A)1195 4030 y Fu(0)1218 4072 y Fy(\))1256 4023 y Fv(\037)1300 3999 y Fg(0)1300 4048 y Fl(\033)r Fk(\()p Fl(i)p Fk(\))1416 4072 y Fw(;)49 b Fy(with)33 b Fw(')p Fy(\()p Fw(g)1864 4087 y Fv(i)1891 4072 y Fy(\))28 b(=)f Fw(g)2111 4030 y Fu(0)2107 4096 y Fv(\033)r Ft(\()p Fv(i)p Ft(\))2233 4072 y Fw(;)17 b(\037)2338 4087 y Fv(i)2366 4072 y Fw(')2430 4030 y Fu(\000)p Ft(1)2552 4072 y Fy(=)27 b Fw(\037)2716 4030 y Fu(0)2716 4096 y Fv(\033)r Ft(\()p Fv(i)p Ft(\))2842 4072 y Fw(;)49 b Fy(for)33 b(all)d(1)d Fx(\024)i Fw(i)f Fx(\024)g Fw(\022)s(:)-180 4303 y Fy(Moreo)m(v)m(er,)j(since)d(for)f (all)f Fw(i)p Fy(,)k Fx(P)940 4318 y Fv(g)974 4328 y Fl(i)1000 4318 y Fv(;)p Ft(1)1059 4303 y Fy(\()p Fw(A)p Fy(\))1208 4267 y Fv(\037)1252 4277 y Fl(i)1310 4303 y Fy(and)e Fx(P)1564 4320 y Fv(g)1600 4297 y Fg(0)1598 4346 y Fl(\033)r Fk(\()p Fl(i)p Fk(\))1710 4320 y Fv(;)p Ft(1)1769 4303 y Fy(\()p Fw(A)p Fy(\))1918 4254 y Fv(\037)1962 4231 y Fg(0)1962 4280 y Fl(\033)r Fk(\()p Fl(i)p Fk(\))2106 4303 y Fy(are)g(one-dimensional)d(with)i(basis)h Fw(a)3478 4318 y Fv(i)3535 4303 y Fy(and)g Fw(a)3771 4267 y Fu(0)3771 4328 y Fv(i)3799 4303 y Fy(,)h(there)-180 4443 y(are)k(non-zero)f (scalars)h Fw(\013)756 4458 y Fv(i)812 4443 y Fx(2)28 b Fo(|)17 b Fy(with)33 b Fw(\036)p Fy(\()p Fw(a)1363 4458 y Fv(i)1391 4443 y Fy(\))27 b(=)h Fw(\013)1622 4458 y Fv(i)1650 4443 y Fw(a)1701 4407 y Fu(0)1701 4473 y Fv(\033)r Ft(\()p Fv(i)p Ft(\))1827 4443 y Fy(,)33 b(for)f(all)e(1)e Fx(\024)g Fw(i)g Fx(\024)g Fw(\022)s Fy(.)-80 4582 y(Then)i(the)f (elemen)m(ts)g Fw(\036)p Fy(\()p Fw(a)877 4597 y Fv(i)905 4582 y Fy(\))p Fw(;)17 b Fy(1)27 b Fx(\024)h Fw(i)g Fx(\024)g Fw(\022)s Fy(,)i(satisfy)f(the)g(Serre)g(relations)f(\(4.11\))o(,)i (and)e(they)i(satisfy)g(\(4.12\))e(if)g(and)-180 4722 y(only)h(if)g(the)i(triple)d(\()p Fw(';)17 b(\033)n(;)g Fy(\()p Fw(\013)884 4737 y Fv(i)912 4722 y Fy(\)\))30 b(is)g(an)f(isomorphism)f(of)h(generic)h(data.)43 b(Th)m(us)31 b(the)g(map)e(Isom\()p Fw(U)10 b Fy(\()p Fx(D)s Fy(\))p Fw(;)17 b(U)10 b Fy(\()p Fx(D)3846 4686 y Fu(0)3869 4722 y Fy(\)\))27 b Fx(!)-180 4861 y Fy(Isom\()p Fx(D)s Fw(;)17 b Fx(D)266 4825 y Fu(0)288 4861 y Fy(\))37 b(in)g(the)g(theorem)g(is)g (w)m(ell-de\014ned)h(and)f(injectiv)m(e.)58 b(Surjectivit)m(y)37 b(of)g(this)g(map)f(follo)m(ws)g(from)g(the)-180 5001 y(description)c(of)g(the)h(Hopf)g(algebras)f Fw(U)10 b Fy(\()p Fx(D)s Fy(\))32 b(and)h Fw(U)10 b Fy(\()p Fx(D)1865 4965 y Fu(0)1888 5001 y Fy(\))33 b(in)f(Theorem)h(4.2.)1357 b Fi(\003)-80 5201 y Fy(The)33 b(main)f(reason)h(wh)m(y)h(the)g(pro)s (of)e(of)g(the)h(preceding)h(theorem)e(w)m(orks)i(is)f(the)g(kno)m (wledge)h(of)e(the)i(coradical)-180 5317 y(\014ltration.)41 b(The)34 b(same)e(ideas)h(allo)m(w)e(to)h(determine)g(all)f(Hopf)h (subalgebras)h(of)f Fw(U)10 b Fy(\()p Fx(D)s Fy(\).)p eop %%Page: 18 18 18 17 bop -180 0 a Fp(18)846 b(NICOL)1001 -19 y(\023)991 0 y(AS)24 b(ANDR)n(USKIEWITSCH)f(AND)h(HANS-J)2419 -19 y(\177)2409 0 y(UR)n(GEN)f(SCHNEIDER)687 203 y Fy(5.)49 b Fz(Pointed)37 b(Hopf)h(algebras)f(with)h(generic)f(braidings)-80 377 y Fy(W)-8 b(e)42 b(are)g(going)e(to)i(sho)m(w)h(that)f(the)g(class) g(of)g(Hopf)g(algebras)f(describ)s(ed)i(in)e(the)h(previous)h(section)f (has)g(an)-180 494 y(in)m(trinsic)31 b(description.)-80 610 y(The)45 b(follo)m(wing)c(k)m(ey)k(Lemma)e(implies)f(that)h(p)s (oin)m(ted)h(Hopf)g(algebras)f(b)s(elonging)f(to)i(a)g(natural)f(class) h(are)-180 726 y(generated)33 b(b)m(y)h(group-lik)m(e)d(and)i(sk)m(ew)h (primitiv)m(e)d(elemen)m(ts.)-180 887 y FC(Lemma)53 b(5.1.)c Fs(\(a\).)83 b(L)-5 b(et)48 b Fw(S)57 b Fy(=)51 b Fx(\010)1201 902 y Fv(n)p Fu(2)p Fh(N)1343 887 y Fw(S)6 b Fy(\()p Fw(n)p Fy(\))48 b Fs(b)-5 b(e)47 b(a)h(gr)-5 b(ade)g(d)47 b(br)-5 b(aide)g(d)46 b(Hopf)i(algebr)-5 b(a)47 b(such)g(that)h Fw(S)6 b Fy(\(0\))51 b(=)g Fo(C)20 b Fw(:)p Fy(1)p Fs(,)-180 1026 y Fw(V)57 b Fy(:=)36 b Fw(S)6 b Fy(\(1\))39 b Fs(is)g (\014nite-dimensional)d(and)j(gener)-5 b(ates)39 b Fw(S)45 b Fs(as)39 b(an)f(algebr)-5 b(a.)57 b(Assume)39 b(that)h Fw(S)45 b Fs(has)39 b(\014nite)g(Gelfand-)-180 1165 y(Kiril)5 b(lov)34 b(dimension)f(and)i(that)g Fw(V)56 b Fs(has)35 b(p)-5 b(ositive)34 b(br)-5 b(aiding.)44 b(Then)34 b Fw(S)40 b Fs(is)35 b(a)g(Nichols)f(algebr)-5 b(a.)-80 1305 y(\(b\).)48 b(L)-5 b(et)37 b Fw(R)g Fs(b)-5 b(e)36 b(as)g Fw(S)42 b Fs(in)36 b(\(a\),)g(exc)-5 b(ept)36 b(that)h(we)f(assume)g Fw(P)14 b Fy(\()p Fw(R)q Fy(\))29 b(=)h Fw(R)q Fy(\(1\))37 b Fs(inste)-5 b(ad)35 b(of)h(gener)-5 b(ation)36 b(in)g(de)-5 b(gr)g(e)g(e)35 b(1.)-180 1444 y(Then)f Fw(R)i Fs(is)f(a)f(Nichols)h(algebr)-5 b(a.)-180 1635 y(Pr)g(o)g(of.)41 b Fy(\(a\).)i Fj(B)p Fy(\()p Fw(V)22 b Fy(\))31 b(has)i(\014nite)e(Gelfand-Kirillo)m(v)c(dimension)k(since)h (it)f(is)h(a)f(quotien)m(t)h(of)g Fw(S)6 b Fy(.)43 b(Assume)33 b(\014rst)f(that)-180 1775 y(the)38 b(matrix)f(is)g(indecomp)s(osable.) 59 b(W)-8 b(e)38 b(can)g(then)h(apply)e(Theorem)h(2.13;)i(let)e(\()p Fw(a)2928 1790 y Fv(ij)2988 1775 y Fy(\),)i(\()p Fw(d)3182 1790 y Ft(1)3221 1775 y Fw(;)17 b(:)g(:)g(:)f(;)h(d)3491 1790 y Fv(\022)3529 1775 y Fy(\))38 b(and)g Fw(q)j Fy(suc)m(h)-180 1914 y(that)32 b Fw(q)74 1929 y Fv(ij)135 1914 y Fw(q)178 1929 y Fv(j)t(i)267 1914 y Fy(=)27 b Fw(q)417 1878 y Fv(d)453 1888 y Fl(i)480 1878 y Fv(a)517 1888 y Fl(ij)609 1914 y Fy(for)32 b(all)e Fw(i)e Fx(6)p Fy(=)g Fw(j)38 b Fy(and)33 b Fw(q)1369 1929 y Fv(ii)1449 1914 y Fy(=)27 b Fw(q)1599 1878 y Fv(d)1635 1888 y Fl(ii)1688 1914 y Fy(.)-80 2054 y(Let)33 b Fw(i)c Fx(6)p Fy(=)g Fw(j)6 b Fy(.)45 b(W)-8 b(e)34 b(claim)d(that)i Fw(z)1067 2069 y Ft(2)1135 2054 y Fy(=)c(ad)1359 2069 y Fv(c)1394 2054 y Fy(\()p Fw(x)1487 2069 y Fv(i)1516 2054 y Fy(\))1554 2018 y Ft(1)p Fu(\000)p Fv(a)1681 2028 y Fl(ij)1740 2054 y Fy(\()p Fw(x)1833 2069 y Fv(j)1870 2054 y Fy(\))g(=)g(0)k(in)f Fw(S)6 b Fy(.)45 b(Indeed,)35 b(let)e Fw(z)2908 2069 y Ft(1)2976 2054 y Fy(=)c Fw(x)3136 2069 y Fv(i)3165 2054 y Fy(,)k(supp)s(ose)i(that)e Fw(z)3850 2069 y Ft(2)3918 2054 y Fx(6)p Fy(=)c(0)-180 2193 y(and)k(consider)g(the)g(t)m(w)m (o-dimensional)d(subspace)k Fw(W)47 b Fy(of)32 b Fw(S)38 b Fy(generated)33 b(b)m(y)h(the)f(primitiv)m(e)d(elemen)m(ts)j Fw(z)3643 2208 y Ft(1)3715 2193 y Fy(and)g Fw(z)3950 2208 y Ft(2)3990 2193 y Fy(.)-80 2333 y(W)-8 b(e)42 b(claim)d(that)j Fj(B)p Fy(\()p Fw(W)14 b Fy(\))41 b(has)h(\014nite)f(Gelfand-Kirillo)m (v)c(dimension.)70 b(F)-8 b(or,)43 b(let)e Fw(T)55 b Fy(b)s(e)42 b(the)g(subalgebra)g(of)f Fw(S)-180 2472 y Fy(generated)28 b(b)m(y)g Fw(W)14 b Fy(;)29 b(then)f(the)f(graded)h (Hopf)f(algebra)f(gr)16 b(\()p Fw(T)e Fy(#)p Fo(C)20 b Fy(\000\))33 b(has)27 b(\014nite)g(Gelfand-Kirillo)m(v)c(dimension,)k (and)-180 2612 y(con)m(tains)33 b Fj(B)p Fy(\()p Fw(W)14 b Fy(\).)-80 2751 y(Also,)32 b(the)h(braiding)d(of)j Fw(W)46 b Fy(is)32 b(giv)m(en)h(b)m(y)g(the)g(matrix:)566 2904 y Fn( )765 3002 y Fw(q)808 3017 y Fv(ii)1347 3002 y Fw(q)1394 2948 y Ft(1)p Fu(\000)p Fv(a)1521 2958 y Fl(ij)1390 3027 y Fv(ii)1580 3002 y Fw(q)1623 3017 y Fv(ij)644 3153 y Fw(q)691 3099 y Ft(1)p Fu(\000)p Fv(a)818 3109 y Fl(ij)687 3179 y Fv(ii)878 3153 y Fw(q)921 3168 y Fv(j)t(i)1065 3153 y Fw(q)1112 3099 y Ft(\(1)p Fu(\000)p Fv(a)1266 3109 y Fl(ij)1321 3099 y Ft(\))1348 3076 y Fk(2)1108 3179 y Fv(ii)1387 3153 y Fw(q)1434 3099 y Ft(1)p Fu(\000)p Fv(a)1561 3109 y Fl(ij)1430 3179 y Fv(ij)1621 3153 y Fw(q)1668 3099 y Ft(1)p Fu(\000)p Fv(a)1795 3109 y Fl(ij)1664 3179 y Fv(j)t(i)1854 3153 y Fw(q)1897 3168 y Fv(j)t(j)1966 2904 y Fn(!)2073 3074 y Fy(=)2176 2904 y Fn( )2426 3008 y Fw(q)2473 2972 y Fv(d)2509 2982 y Fl(i)2793 3008 y Fw(q)2840 2972 y Fv(d)2876 2982 y Fl(i)2902 2972 y Ft(\(1)p Fu(\000)p Fv(a)3056 2982 y Fl(ij)3112 2972 y Ft(\))3144 3008 y Fw(q)3187 3023 y Fv(ij)2255 3147 y Fw(q)2302 3111 y Fv(d)2338 3121 y Fl(i)2365 3111 y Ft(\(1)p Fu(\000)p Fv(a)2519 3121 y Fl(ij)2574 3111 y Ft(\))2606 3147 y Fw(q)2649 3162 y Fv(j)t(i)2797 3147 y Fw(q)2844 3111 y Fv(d)2880 3121 y Fl(i)2906 3111 y Fu(\000)p Fv(d)2997 3121 y Fl(i)3024 3111 y Fv(a)3061 3121 y Fl(ij)3116 3111 y Ft(+)p Fv(d)3207 3121 y Fl(j)3248 2904 y Fn(!)-180 3315 y Fy(By)49 b(Theorem)g(2.11)f(and)h(Lemma)f(2.1,) k(there)e(exists)f Fw(k)59 b Fx(\025)c Fy(0)49 b(suc)m(h)h(that)f(1)55 b(=)g Fw(q)3051 3279 y Fv(d)3087 3289 y Fl(i)3113 3279 y Fv(k)r Ft(+2)p Fv(d)3278 3289 y Fl(i)3305 3279 y Ft(\(1)p Fu(\000)p Fv(a)3459 3289 y Fl(ij)3514 3279 y Ft(\))3546 3315 y Fw(q)3589 3330 y Fv(ij)3650 3315 y Fw(q)3693 3330 y Fv(j)t(i)3754 3315 y Fy(,)e(hence)-180 3454 y(0)27 b(=)h Fw(d)51 3469 y Fv(i)79 3454 y Fw(k)d Fy(+)d(2)p Fw(d)353 3469 y Fv(i)381 3454 y Fy(\(1)g Fx(\000)g Fw(a)640 3469 y Fv(ij)701 3454 y Fy(\))g(+)g Fw(d)910 3469 y Fv(i)938 3454 y Fw(a)989 3469 y Fv(ij)1077 3454 y Fy(=)28 b Fw(d)1232 3469 y Fv(i)1260 3454 y Fy(\()p Fw(k)d Fy(+)d(2)g Fx(\000)g Fw(a)1693 3469 y Fv(ij)1754 3454 y Fy(\),)33 b(a)f(con)m(tradiction.)42 b(This)33 b(sho)m(ws)h(that)f Fw(z)3324 3469 y Ft(2)3391 3454 y Fy(=)28 b(0.)-80 3594 y(Therefore,)43 b(w)m(e)e(ha)m(v)m(e)g(an) f(epimorphism)e(of)h(braided)h(graded)g(Hopf)g(algebras)f Fj(B)p Fy(\()p Fw(V)22 b Fy(\))40 b Fx(!)g Fw(S)6 b Fy(,)42 b(b)m(y)f(Step)f(I)s(I)g(of)-180 3733 y(Theorem)33 b(4.2,)f(whic)m(h)h (is)f(the)h(iden)m(tit)m(y)g(in)f(degree)h(1.)43 b(Hence)34 b Fj(B)p Fy(\()p Fw(V)22 b Fy(\))27 b Fx(')h Fw(S)6 b Fy(.)-80 3915 y(Assume)24 b(no)m(w)g(that)g(the)g(matrix)e(is)h(decomp) s(osable.)40 b(Let)24 b Fw(i)p Fy(,)i Fw(j)k Fy(b)s(elong)22 b(to)i(di\013eren)m(t)g(comp)s(onen)m(ts;)j(in)c(particular)-180 4054 y Fw(q)-137 4069 y Fv(ij)-76 4054 y Fw(q)-33 4069 y Fv(j)t(i)57 4054 y Fy(=)30 b(1.)47 b(W)-8 b(e)34 b(claim)d(that)j Fw(x)984 4069 y Fv(i)1013 4054 y Fw(x)1068 4069 y Fv(j)1134 4054 y Fy(=)c Fw(q)1283 4069 y Fv(ij)1344 4054 y Fw(x)1399 4069 y Fv(j)1436 4054 y Fw(x)1491 4069 y Fv(i)1519 4054 y Fy(.)47 b(If)34 b(not,)g(let)f Fw(z)2081 4069 y Ft(1)2151 4054 y Fy(:=)d Fw(x)2339 4069 y Fv(i)2401 4054 y Fy(and)k Fw(z)2637 4069 y Ft(2)2706 4054 y Fy(:=)c Fw(x)2894 4069 y Fv(i)2923 4054 y Fw(x)2978 4069 y Fv(j)3038 4054 y Fx(\000)23 b Fw(q)3181 4069 y Fv(ij)3242 4054 y Fw(x)3297 4069 y Fv(j)3334 4054 y Fw(x)3389 4069 y Fv(i)3451 4054 y Fy(is)33 b(primitiv)m(e)f(b)m(y)-180 4194 y(Lemma)e(2.1)h(\(b\).)43 b(Let)32 b Fw(z)742 4209 y Ft(1)809 4194 y Fy(=)c Fw(x)968 4209 y Fv(i)1028 4194 y Fy(and)k(consider)f(as)h(b)s(efore)g(the)f (subspace)j Fw(W)45 b Fy(of)31 b Fw(S)37 b Fy(generated)32 b(b)m(y)h Fw(z)3546 4209 y Ft(1)3617 4194 y Fy(and)f Fw(z)3851 4209 y Ft(2)3890 4194 y Fy(.)43 b(As)-180 4333 y(b)s(efore,)33 b Fj(B)p Fy(\()p Fw(W)14 b Fy(\))31 b(has)i(\014nite)f (Gelfand-Kirillo)m(v)c(dimension.)42 b(No)m(w)33 b(the)g(braiding)d(of) i Fw(W)46 b Fy(is)32 b(giv)m(en)g(b)m(y)i(the)e(matrix:)1283 4486 y Fn( )1366 4590 y(e)-59 b Fw(q)1405 4605 y Ft(11)1567 4590 y Fn(e)g Fw(q)1606 4605 y Ft(12)1366 4729 y Fn(e)g Fw(q)1405 4744 y Ft(21)1567 4729 y Fn(e)g Fw(q)1606 4744 y Ft(22)1681 4486 y Fn(!)1787 4657 y Fy(:=)1918 4486 y Fn( )2049 4590 y Fw(q)2092 4605 y Fv(ii)2283 4590 y Fw(q)2326 4605 y Fv(ii)2379 4590 y Fw(q)2422 4605 y Fv(ij)1997 4729 y Fw(q)2040 4744 y Fv(ii)2092 4729 y Fw(q)2135 4744 y Fv(j)t(i)2279 4729 y Fw(q)2322 4744 y Fv(ii)2374 4729 y Fw(q)2417 4744 y Fv(j)t(j)2487 4486 y Fn(!)2582 4657 y Fw(:)-180 4898 y Fy(By)39 b(Theorem)f(2.11)f(again,)h(there)h(exists) g Fw(k)h Fx(\025)d Fy(0)h(suc)m(h)i(that)d(1)g(=)g Fw(q)2411 4857 y Fv(k)r Ft(+2)2407 4924 y Fv(ii)2544 4898 y Fw(q)2587 4913 y Fv(ij)2648 4898 y Fw(q)2691 4913 y Fv(j)t(i)2788 4898 y Fy(=)g Fw(q)2948 4857 y Fv(k)r Ft(+2)2944 4924 y Fv(ii)3081 4898 y Fy(,)i(a)f(con)m(tradiction.)59 b(This)-180 5038 y(concludes)34 b(the)f(pro)s(of)e(of)h(\(a\).)-80 5177 y(Finally)-8 b(,)24 b(\(a\))h(and)h(\(b\))f(are)h(equiv)-5 b(alen)m(t)25 b(b)m(y)i([AS2,)g(Lemma)d(5.5])h(and)h(the)g (de\014nition)e(of)h(\014nite)h(Gelfand-Kirillo)m(v)-180 5317 y(dimension.)3717 b Fi(\003)p eop %%Page: 19 19 19 18 bop 1010 0 a Fp(A)33 b(CHARA)n(CTERIZA)-6 b(TION)31 b(OF)i(QUANTUM)f(GR)n(OUPS)1112 b(19)-180 203 y FC(Theorem)36 b(5.2.)42 b Fs(L)-5 b(et)34 b Fw(A)h Fs(b)-5 b(e)33 b(a)h(p)-5 b(ointe)g(d)34 b(Hopf)g(algebr)-5 b(a)34 b(with)g(ab)-5 b(elian)33 b(c)-5 b(or)g(adic)g(al)33 b(and)h(diagr)-5 b(am)33 b Fw(R)q Fs(.)44 b(Assume)35 b(that)-180 342 y Fw(R)q Fy(\(1\))g Fs(is)f(\014nite-dimensional)f(with)h(p)-5 b(ositive)35 b(br)-5 b(aiding.)43 b(Then)34 b(the)h(fol)5 b(lowing)34 b(ar)-5 b(e)34 b(e)-5 b(quivalent:)-80 482 y(\(a\).)44 b Fw(A)35 b Fs(is)f(a)h(domain)f(with)h(\014nite)f (Gelfand-Kiril)5 b(lov)34 b(dimension.)-80 621 y(\(b\).)50 b(The)36 b(gr)-5 b(oup)36 b Fy(\000)c(:=)f Fw(G)p Fy(\()p Fw(A)p Fy(\))37 b Fs(is)f(fr)-5 b(e)g(e)37 b(ab)-5 b(elian)35 b(of)i(\014nite)f(r)-5 b(ank,)37 b(and)f(ther)-5 b(e)37 b(exist)g(a)f(p)-5 b(ositive)36 b(datum)h Fx(D)i Fs(for)e Fy(\000)-180 761 y Fs(such)e(that)g Fw(A)28 b Fx(')g Fw(U)10 b Fy(\()p Fx(D)s Fy(\))35 b Fs(as)f(Hopf)h(algebr)-5 b(as.)-180 965 y(Pr)g(o)g(of.)41 b Fy(\(b\))60 b(=)-17 b Fx(\))60 b Fy(\(a\):)44 b(this)32 b(is)g(Theorem)h(4.2.)-80 1105 y(\(a\))67 b(=)-17 b Fx(\))68 b Fy(\(b\).)53 b(By)36 b([KL,)g(6.5],)g(gr)16 b Fw(A)36 b Fy(has)g(\014nite)f(GK-dimension;)f (hence)j(b)s(oth)f Fw(R)g Fy(and)g Fo(|)-9 b Fy(\000)30 b(also)k(ha)m(v)m(e.)54 b(It)35 b(is)-180 1244 y(clear)j(then)h(that)g (\000)f(should)h(b)s(e)g(a)f(free)h(ab)s(elian)e(group)h(of)g(\014nite) h(rank,)h(sa)m(y)g Fw(s)p Fy(.)61 b(Consider)39 b(the)g(diagram)e Fw(R)i Fy(of)-180 1384 y Fw(A)p Fy(.)k(F)-8 b(rom)31 b(Theorem)i(2.13)e(and)h(Lemma)f(5.1,)h(w)m(e)h(conclude)g(the)g (existence)g(of)f(the)h(\014nite)e(Cartan)i(matrix)d(\()p Fw(a)3946 1399 y Fv(ij)4007 1384 y Fy(\),)-180 1523 y(the)39 b(family)d(\()p Fw(q)379 1538 y Fv(I)419 1523 y Fy(\))457 1538 y Fv(I)5 b Fu(2X)604 1523 y Fy(,)39 b(and)g(the)f(elemen)m(ts)h Fw(g)1491 1538 y Ft(1)1530 1523 y Fw(;)17 b(:)g(:)g(:)f(;)h(g)1796 1538 y Fv(\022)1872 1523 y Fx(2)38 b Fy(\000,)h Fw(\037)2164 1538 y Ft(1)2204 1523 y Fw(;)17 b(:)g(:)g(:)f(;)h(\037)2484 1538 y Fv(\022)2560 1523 y Fx(2)2667 1498 y Fn(b)2664 1523 y Fy(\000)38 b(satisfying)h(\(4.1\))o(,)h(and)e(suc)m(h)i(that) -180 1663 y(no)f Fw(q)5 1678 y Fv(I)84 1663 y Fy(is)g(a)g(ro)s(ot)f(of) h(1)f(\(in)h(fact)g Fw(q)1098 1678 y Fv(I)1176 1663 y Fw(>)g Fy(0)g(and)g(not)g(1)g(for)g(all)e Fw(I)8 b Fy(\),)40 b Fw(R)g Fy(=)f Fj(B)p Fy(\()p Fw(V)21 b Fy(\))39 b(where)i Fw(V)60 b Fx(2)3318 1626 y Fh(|)-14 b Ft(\000)3318 1688 y Fh(|)g Ft(\000)3403 1663 y Fx(Y)8 b(D)42 b Fy(has)d(a)g(basis)-180 1802 y Fw(x)-125 1817 y Fv(i)-69 1802 y Fx(2)28 b Fw(V)104 1766 y Fv(\037)148 1776 y Fl(i)82 1827 y Fv(g)116 1837 y Fl(i)178 1802 y Fw(;)17 b Fy(1)27 b Fx(\024)i Fw(i)f Fx(\024)g Fw(\022)s Fy(.)-80 1942 y(Since)34 b(gr)p Fw(A)367 1914 y Fx(\030)368 1946 y Fy(=)475 1942 y Fj(B)p Fy(\()p Fw(V)22 b Fy(\)#)p Fo(|)-9 b Fy(\000)28 b(as)35 b(graded)g(Hopf)f (algebras,)g(and)h Fw(\037)2295 1957 y Fv(i)2323 1942 y Fy(\()p Fw(g)2408 1957 y Fv(i)2436 1942 y Fy(\))c Fx(6)p Fy(=)f(1)k(for)g(all)e(1)f Fx(\024)g Fw(i)g Fx(\024)h Fw(\022)s Fy(,)j(it)e(follo)m(ws)g(from)-180 2081 y(Lemma)e(4.3)h(that) h(the)g(\014rst)g(term)f(of)g(the)h(coradical)e(\014ltration)f(of)i Fw(A)h Fy(is)-180 2273 y(\(5.1\))1265 b Fw(A)1359 2288 y Ft(1)1426 2273 y Fy(=)27 b Fw(A)1602 2288 y Ft(0)1664 2273 y Fx(\010)1864 2179 y Fn(M)1764 2391 y Fv(g)r Fu(2)p Ft(\000)p Fv(;)p Ft(1)p Fu(\024)p Fv(i)p Fu(\024)p Fv(\022)2131 2273 y Fx(P)2200 2288 y Fv(g)r(g)2270 2298 y Fl(i)2296 2288 y Fv(;g)2356 2273 y Fy(\()p Fw(A)p Fy(\))2505 2232 y Fv(\037)2549 2242 y Fl(i)2579 2273 y Fw(:)-80 2550 y Fy(W)-8 b(e)42 b(can)g(then)h(c)m(ho)s(ose)f Fw(a)886 2565 y Fv(i)958 2550 y Fx(2)i(P)1137 2565 y Fv(g)1171 2575 y Fl(i)1197 2565 y Fv(;)p Ft(1)1257 2550 y Fy(\()p Fw(A)p Fy(\))1406 2514 y Fv(\037)1450 2524 y Fl(i)1522 2550 y Fy(suc)m(h)f(that)f(the)g(class)g(of)f Fw(a)2558 2565 y Fv(i)2629 2550 y Fy(in)g(gr)16 b Fw(A)p Fy(\(1\))41 b(coincides)h(with)g Fw(x)3803 2565 y Fv(i)3831 2550 y Fy(.)72 b(Let)-180 2689 y Fw(y)-132 2704 y Ft(1)-93 2689 y Fw(;)17 b Fx(\001)g(\001)g(\001)31 b Fw(;)17 b(y)192 2704 y Fv(s)261 2689 y Fy(b)s(e)32 b(free)h(generators)g(of)g Fw(G)p Fy(\()p Fw(A)p Fy(\).)43 b(It)33 b(is)f(clear)g(that)g (relations)f(\(4.9\))h(and)h(\(4.10\))f(hold.)-80 2829 y(Let)g Fw(i)c Fx(6)p Fy(=)g Fw(j)6 b Fy(.)43 b(W)-8 b(e)33 b(claim:)-80 3021 y(\(i\).)42 b(There)34 b(exists)f(no)g Fw(`)p Fy(,)f(1)c Fx(\024)g Fw(`)f Fx(\024)i Fw(\022)s Fy(,)j(suc)m(h)i(that)f Fw(g)1826 2967 y Ft(1)p Fu(\000)p Fv(a)1953 2977 y Fl(ij)1822 3047 y Fv(i)2012 3021 y Fw(g)2059 3036 y Fv(j)2123 3021 y Fy(=)27 b Fw(g)2273 3036 y Fv(`)2306 3021 y Fy(,)32 b Fw(\037)2426 2967 y Ft(1)p Fu(\000)p Fv(a)2553 2977 y Fl(ij)2426 3047 y Fv(i)2613 3021 y Fw(\037)2674 3036 y Fv(j)2738 3021 y Fy(=)c Fw(\037)2903 3036 y Fv(`)2936 3021 y Fy(.)-80 3213 y(\(ii\).)41 b(If)33 b Fw(i)28 b Fx(\030)g Fw(j)6 b Fy(,)32 b(then)i Fw(\037)773 3159 y Ft(1)p Fu(\000)p Fv(a)900 3169 y Fl(ij)773 3239 y Fv(i)959 3213 y Fw(\037)1020 3228 y Fv(j)1084 3213 y Fx(6)p Fy(=)28 b Fw(")p Fy(.)-80 3406 y(W)-8 b(e)33 b(pro)m(v)m(e)g(\(i\).)43 b(Assume)33 b(that)g Fw(g)1148 3352 y Ft(1)p Fu(\000)p Fv(a)1275 3362 y Fl(ij)1144 3431 y Fv(i)1333 3406 y Fw(g)1380 3421 y Fv(j)1444 3406 y Fy(=)28 b Fw(g)1595 3421 y Fv(`)1628 3406 y Fy(,)k Fw(\037)1748 3352 y Ft(1)p Fu(\000)p Fv(a)1875 3362 y Fl(ij)1748 3431 y Fv(i)1935 3406 y Fw(\037)1996 3421 y Fv(j)2060 3406 y Fy(=)c Fw(\037)2225 3421 y Fv(`)2290 3406 y Fy(for)k(some)h Fw(`)p Fy(.)43 b(Then)682 3599 y Fw(q)729 3553 y Fv(d)765 3563 y Fl(i)791 3553 y Fv(a)828 3565 y Fl(i`)725 3626 y Fv(I)913 3599 y Fy(=)27 b Fx(h)p Fw(\037)1116 3614 y Fv(`)1149 3599 y Fw(;)17 b(g)1240 3614 y Fv(i)1267 3599 y Fx(ih)p Fw(\037)1406 3614 y Fv(i)1434 3599 y Fw(;)g(g)1525 3614 y Fv(`)1558 3599 y Fx(i)27 b Fy(=)h Fw(q)1775 3545 y Ft(2)p Fv(d)1846 3555 y Fl(i)1872 3545 y Ft(\(1)p Fu(\000)p Fv(a)2026 3555 y Fl(ij)2082 3545 y Ft(\))1771 3626 y Fv(I)2114 3599 y Fx(h)p Fw(\037)2214 3614 y Fv(j)2250 3599 y Fw(;)17 b(g)2341 3614 y Fv(i)2369 3599 y Fx(ih)p Fw(\037)2508 3614 y Fv(i)2536 3599 y Fw(;)g(g)2627 3614 y Fv(j)2662 3599 y Fx(i)28 b Fy(=)f Fw(q)2879 3545 y Fv(d)2915 3555 y Fl(i)2942 3545 y Ft(\(2)p Fu(\000)p Fv(a)3096 3555 y Fl(ij)3152 3545 y Ft(\))2875 3626 y Fv(I)3183 3599 y Fy(;)-180 3791 y(w)m(e)41 b(conclude)g(that)f(2)h(=)f Fw(a)856 3806 y Fv(ij)944 3791 y Fy(+)27 b Fw(a)1098 3806 y Fv(i`)1156 3791 y Fy(.)66 b(The)41 b(only)f(p)s(ossibilit)m(y)e (is)i Fw(a)2308 3806 y Fv(ij)2409 3791 y Fy(=)h(0)f(and)g Fw(l)j Fy(=)e Fw(i)p Fy(.)67 b(Then)41 b Fw(g)3437 3806 y Fv(j)3514 3791 y Fy(=)g(1)f(whic)m(h)g(is)-180 3931 y(imp)s(ossible.)-80 4070 y(W)-8 b(e)37 b(pro)m(v)m(e)h(\(ii\).)54 b(Assume)38 b(that)f Fw(\037)1215 4016 y Ft(1)p Fu(\000)p Fv(a)1342 4026 y Fl(ij)1215 4096 y Fv(i)1401 4070 y Fw(\037)1462 4085 y Fv(j)1534 4070 y Fy(=)e Fw(")p Fy(,)i Fw(i)f Fx(6)p Fy(=)e Fw(j)6 b Fy(,)38 b Fw(i)e Fx(\030)f Fw(j)6 b Fy(.)56 b(Ev)-5 b(aluating)35 b(at)i Fw(g)3022 4085 y Fv(i)3050 4070 y Fy(,)h(w)m(e)g(get)e(1)f(=)g Fw(q)3671 4016 y Ft(1)p Fu(\000)p Fv(a)3798 4026 y Fl(ij)3667 4096 y Fv(ii)3857 4070 y Fw(q)3900 4085 y Fv(ij)3996 4070 y Fy(=)-180 4210 y Fw(q)-137 4225 y Fv(ii)-85 4210 y Fy(\()p Fw(q)-4 4225 y Fv(ij)57 4210 y Fw(q)100 4225 y Fv(j)t(i)161 4210 y Fy(\))199 4173 y Fu(\000)p Ft(1)293 4210 y Fw(q)336 4225 y Fv(ij)431 4210 y Fy(=)e Fw(q)583 4225 y Fv(ii)635 4210 y Fw(q)682 4168 y Fu(\000)p Ft(1)678 4235 y Fv(j)t(i)777 4210 y Fy(,)k(so)f(that)g Fw(q)1222 4225 y Fv(ii)1308 4210 y Fy(=)d Fw(q)1460 4225 y Fv(j)t(i)1521 4210 y Fy(.)54 b(Ev)-5 b(aluating)34 b(at)i Fw(g)2267 4225 y Fv(j)2303 4210 y Fy(,)h(w)m(e)g(get)f(1)d(=)h Fw(q)2919 4155 y Ft(1)p Fu(\000)p Fv(a)3046 4165 y Fl(ij)2915 4235 y Fv(j)t(i)3105 4210 y Fw(q)3148 4225 y Fv(j)t(j)3217 4210 y Fy(;)k(hence)f Fw(q)3599 4225 y Fv(j)t(j)3702 4210 y Fy(=)d Fw(q)3859 4155 y Fv(a)3896 4165 y Fl(ij)3951 4155 y Fu(\000)p Ft(1)3855 4235 y Fv(ii)4045 4210 y Fy(.)-180 4349 y(Hence)g(0)27 b(=)h Fw(d)341 4364 y Fv(i)369 4349 y Fy(\(1)22 b Fx(\000)g Fw(a)628 4364 y Fv(ij)689 4349 y Fy(\))g(+)g Fw(d)898 4364 y Fv(j)934 4349 y Fy(;)33 b(this)f(is)g(a)h(con)m(tradiction.)-80 4555 y(If)c Fw(i)f Fx(6)p Fy(=)f Fw(j)6 b Fy(,)30 b(then)g(\(ad)16 b Fw(a)708 4570 y Fv(i)736 4555 y Fy(\))774 4519 y Ft(1)p Fu(\000)p Fv(a)901 4529 y Fl(ij)961 4555 y Fw(a)1012 4570 y Fv(j)1076 4555 y Fx(2)28 b(P)1239 4601 y Fv(g)1275 4553 y Fk(1)p Fg(\000)p Fl(a)1387 4568 y(ij)1273 4623 y(i)1446 4601 y Fv(g)1480 4611 y Fl(j)1512 4601 y Fv(;)p Ft(1)1571 4555 y Fy(\()p Fw(H)8 b Fy(\))1736 4519 y Fv(\037)1780 4470 y Fk(1)p Fg(\000)p Fl(a)1892 4486 y(ij)1780 4541 y(i)1950 4519 y Fv(\037)1994 4529 y Fl(j)2060 4555 y Fy(b)m(y)30 b(Lemma)e(2.1)g(\(b\).)43 b(If)29 b Fw(i)f Fx(\030)g Fw(j)6 b Fy(,)30 b(taking)e(in)m(to)g(accoun)m(t)-180 4706 y(\(5.1\),)k(\(i\))g(and)g(\(ii\),)f(w)m(e)j(see)f(that)g(the)g (quan)m(tum)g(Serre)g(relations)e(\(4.11\))h(hold)g(in)f Fw(A)p Fy(.)-80 4898 y(Finally)-8 b(,)36 b(assume)j(that)f Fw(i)g Fx(6\030)f Fw(j)6 b Fy(;)41 b(if)c(0)g Fx(6)p Fy(=)g(\(ad)16 b Fw(a)1638 4913 y Fv(i)1667 4898 y Fy(\))p Fw(a)1756 4913 y Fv(j)1830 4898 y Fx(2)37 b(P)2002 4913 y Fv(g)2036 4923 y Fl(i)2062 4913 y Fv(g)2096 4923 y Fl(j)2129 4913 y Fv(;)p Ft(1)2188 4898 y Fy(\()p Fw(A)p Fy(\))2337 4862 y Fv(\037)2381 4872 y Fl(i)2407 4862 y Fv(\037)2451 4872 y Fl(j)2487 4898 y Fy(,)j(then)f Fw(\037)2843 4913 y Fv(i)2871 4898 y Fw(\037)2932 4913 y Fv(j)3006 4898 y Fy(=)e Fw(")h Fy(b)m(y)i(\(5.1\))e(and)g(\(i\).)59 b(So)-180 5038 y(that)28 b Fw(a)78 5053 y Fv(i)107 5038 y Fw(a)158 5053 y Fv(j)208 5038 y Fx(\000)14 b Fw(\037)360 5053 y Fv(j)398 5038 y Fy(\()p Fw(g)483 5053 y Fv(i)510 5038 y Fy(\))p Fw(a)599 5053 y Fv(j)636 5038 y Fw(a)687 5053 y Fv(i)743 5038 y Fy(=)28 b Fw(\025)904 5053 y Fv(ij)964 5038 y Fy(\(1)14 b Fx(\000)g Fw(g)1203 5053 y Fv(i)1231 5038 y Fw(g)1278 5053 y Fv(j)1314 5038 y Fy(\))29 b(for)f(some)g Fw(\025)1823 5053 y Fv(ij)1911 5038 y Fx(2)g Fo(|)-8 b Fy(,)23 b(where)30 b Fw(\025)2452 5053 y Fv(ij)2540 5038 y Fy(=)e(0)g(when)i Fw(\037)3033 5053 y Fv(i)3061 5038 y Fw(\037)3122 5053 y Fv(j)3186 5038 y Fx(6)p Fy(=)e Fw(")p Fy(.)42 b(But)28 b(w)m(e)i(can)f(also)-180 5177 y(c)m(ho)s(ose)35 b Fw(\025)188 5192 y Fv(ij)279 5177 y Fy(=)30 b(0)k(when)h Fw(g)771 5192 y Fv(i)799 5177 y Fw(g)846 5192 y Fv(j)913 5177 y Fy(=)30 b(1.)48 b(By)36 b(\(4.7\))o(,)f(w)m(e)g(can)f(rescale)h(a)f(generator)g Fw(a)2772 5192 y Fv(i)2834 5177 y Fy(with)g Fw(\025)3115 5192 y Fv(ij)3206 5177 y Fx(6)p Fy(=)c(0)k(to)g(ha)m(v)m(e)h Fw(\025)3799 5192 y Fv(ij)3890 5177 y Fy(=)30 b(1.)-180 5317 y(Hence,)k(\()p Fw(\025)232 5332 y Fv(ij)292 5317 y Fy(\))f(is)f(a)g(linking)f(datum)h(for)g(\()p Fw(a)1412 5332 y Fv(ij)1472 5317 y Fy(\),)h Fw(g)1617 5332 y Ft(1)1656 5317 y Fw(;)17 b(:)g(:)g(:)f(;)h(g)1922 5332 y Fv(\022)1993 5317 y Fy(and)32 b Fw(\037)2243 5332 y Ft(1)2283 5317 y Fw(;)17 b(:)g(:)g(:)f(;)h(\037)2563 5332 y Fv(\022)2602 5317 y Fy(;)32 b(and)h(\(4.12\))f(holds.)p eop %%Page: 20 20 20 19 bop -180 0 a Fp(20)846 b(NICOL)1001 -19 y(\023)991 0 y(AS)24 b(ANDR)n(USKIEWITSCH)f(AND)h(HANS-J)2419 -19 y(\177)2409 0 y(UR)n(GEN)f(SCHNEIDER)-80 203 y Fy(W)-8 b(e)46 b(ha)m(v)m(e)h(found)f(a)f(p)s(ositiv)m(e)g(datum)g Fx(D)j Fy(for)e(\000)f(and)h(constructed)h(a)f(homomorphism)d(of)i (Hopf)h(algebras)-180 342 y Fw(')g Fy(:)g Fw(U)10 b Fy(\()p Fx(D)s Fy(\))47 b Fx(!)f Fw(A)p Fy(.)76 b(No)m(w)44 b(gr)16 b Fw(')46 b Fy(:)g(gr)16 b Fw(U)10 b Fy(\()p Fx(D)s Fy(\))47 b Fx(!)f Fy(gr)16 b Fw(A)43 b Fy(is)g(an)h(isomorphism)d(b)m(y)j (Theorem)g(4.2;)k(indeed)c(gr)16 b Fw(')43 b Fy(is)-180 482 y(surjectiv)m(e)32 b(and)f(the)g(restriction)e(of)h(gr)16 b Fw(')31 b Fy(to)f(the)h(\014rst)g(term)f(of)h(the)g(coradical)e (\014ltration)f(is)i(injectiv)m(e;)h(th)m(us)h(gr)16 b Fw(')-180 621 y Fy(is)32 b(injectiv)m(e)h([M,)g(Th.)44 b(5.3.1].)f(Hence)34 b Fw(')e Fy(is)g(is)g(an)h(isomorphism.)1734 b Fi(\003)1656 1074 y Fz(References)-180 1252 y FB([AS1])42 b(N.)25 b(Andruskiewitsc)n(h)f(and)g(H.-J.)h(Sc)n(hneider,)f Fe(Lifting)k(of)g(Quantum)e(Line)l(ar)h(Sp)l(ac)l(es)g(and)h(Pointe)l (d)g(Hopf)g(A)n(lgebr)l(as)f(of)h(or)l(der)-9 1372 y Fd(p)33 1342 y Fc(3)70 1372 y FB(,)f(J.)h(Algebra)e Fb(209)h FB(\(1998\),)g(658{691.)-180 1491 y([AS2])p 58 1491 250 4 v 304 w(,)h Fe(Finite)i(quantum)f(gr)l(oups)h(and)g(Cartan)h(matric)l (es)p FB(,)d(Adv.)g(in)g(Math.)f Fb(154)g FB(\(2000\),)g(1{45.)-180 1611 y([AS3])p 58 1611 V 304 w(,)34 b Fe(Lifting)g(of)h(Nichols)g (algebr)l(as)g(of)g(typ)l(e)f Fd(A)1713 1623 y Fc(2)1784 1611 y Fe(and)h(Pointe)l(d)f(Hopf)h(A)n(lgebr)l(as)f(of)h(or)l(der)g Fd(p)3167 1581 y Fc(4)3204 1611 y FB(,)e(in)f("Hopf)g(algebras)e(and)-9 1730 y(quan)n(tum)d(groups",)f(Pro)r(ceedings)g(of)h(the)h(Collo)r (quium)g(in)g(Brussels)e(1998,)g(ed.)h(S.)h(Caenepp)r(el)g(\(2000\),)e (1{16.)-180 1850 y([AS4])p 58 1850 V 304 w(,)i Fe(Finite)i(quantum)f (gr)l(oups)h(over)h(ab)l(elian)g(gr)l(oups)f(of)g(prime)h(exp)l(onent)p FB(,)c(Ann.)h(Sci.)g(Ec.)f(Norm.)h(Sup)r(er.,)f(to)h(app)r(ear.)-180 1969 y([AS5])p 58 1969 V 304 w(,)38 b Fe(Pointe)l(d)g(Hopf)h(A)n(lgebr) l(as)p FB(,)f(in)e(\\Recen)n(t)f(dev)n(elopmen)n(ts)g(in)h(Hopf)g (algebra)e(Theory",)j(MSRI)f(series)e(Cam)n(bridge)-9 2089 y(Univ.)28 b(Press;)e(to)h(app)r(ear.)-180 2209 y([CM])42 b(W.)32 b(Chin)f(and)g(I.)h(Musson,)g Fe(The)i(c)l(or)l(adic) l(al)h(\014ltr)l(ation)e(for)h(quantize)l(d)g(universal)f(enveloping)i (algebr)l(as)p FB(,)f(J.)d(London)g(Math.)-9 2328 y(So)r(c.)c Fb(53)g FB(\(1996\),)g(pp.)h(50{67.)d Fe(Corrigenda)p FB(,)30 b(J.)d(London)g(Math.)h(So)r(c.)g(\(2\))f(61)g(\(2000\),)f (319{320.)-180 2448 y([DCK])42 b(C.)22 b(De)g(Concini)h(and)f(V.)g(G.)h (Kac,)f Fe(R)l(epr)l(esentations)j(of)g(quantum)f(gr)l(oups)h(at)g(r)l (o)l(ots)f(of)i(1)p FB(,)e(in)e(\\Op)r(erator)e(Algebras,)i(Unitary)-9 2567 y(Represen)n(tations,)k(En)n(v)n(eloping)g(Algebras,)g(and)i(In)n (v)-5 b(arian)n(t)26 b(Theory",)g(ed.)i(A.)g(Connes)f Fe(et)i(al)g FB(\(2000\);)d(Birkh\177)-42 b(auser,)26 b(471{506.)-180 2687 y([D])62 b(J.)27 b(Dixmier,)h Fe(Enveloping)j (algebr)l(as)p FB(,)e(American)e(Mathematical)h(So)r(ciet)n(y)-7 b(,)27 b(Pro)n(vidence,)f(RI,)i(\(1996\).)-180 2806 y([Dr])42 b(V.)28 b(Drinfeld,)g Fe(Quantum)g(gr)l(oups)p FB(,)g(Pro)r(ceedings)e (of)h(the)h(ICM)g(Berk)n(eley)e(1986,)g(A.M.S.)-180 2926 y([Ji])59 b(M.)22 b(Jim)n(b)r(o,)i Fe(A)g Fd(q)s Fe(-di\013er)l(enc)l (e)i(analo)l(gue)g(of)g Fd(U)9 b FB(\()p Fa(g)p FB(\))25 b Fe(and)g(the)g(Y)-6 b(ang)25 b(Baxter)g(e)l(quation)p FB(,)f(Lett.)f(Math.)g(Ph)n(ys.)e Fb(10)h FB(\(1985\),)g(pp.)h(63{69.) -180 3045 y([K])60 b(V.)28 b(Kac,)e Fe(In\014nite-dimensional)31 b(Lie)f(algebr)l(as)p FB(,)f(Cam)n(bridge)e(Univ.)h(Press,)e(Third)h (edition,)h(1995.)-180 3165 y([KW])42 b(D.)33 b(Kazhdan)e(and)i(H.)f(W) -7 b(enzl,)35 b Fe(R)l(e)l(c)l(onstructing)e(monoidal)j(c)l(ate)l (gories)p FB(,)f(I.)d(M.)h(Gelfand)g(Seminar)f(111{136,)f(Adv.)i(So)n (viet)-9 3284 y(Math.)27 b Fb(16)h FB(\(1993\),)e(Amer.)i(Math.)f(So)r (c.,)h(Pro)n(vidence,)e(RI.)-180 3404 y([KL])41 b(G.)36 b(Krause)f(and)h(T.)g(Lenagan,)h Fe(Gr)l(owth)h(of)h(A)n(lgebr)l(as)f (and)g(Gelfand-Kiril)t(low)j(Dimension)p FB(,)e(Revised)c(edition,)k (Graduate)-9 3524 y(Studies)28 b(in)g(Mathematics)f(v)n(ol.)g(22,)f (Amer.)i(Math.)g(So)r(c.,)f(1999.)-180 3643 y([KR])41 b(P)-7 b(.)28 b(P)-7 b(.)27 b(Kulish)h(N.)g(Y)-7 b(u.)28 b(Reshetikhin,)59 b Fe(Quantum)28 b(line)l(ar)i(pr)l(oblem)h(for)g(the) f(sine-Gor)l(don)h(e)l(quation)f(and)h(higher)g(r)l(epr)l(esenta-)-9 3763 y(tions)p FB(,)c(Zap.)h(Nauc)n(hn.)f(Sem.)h(Leningrad.)f(Otdel.)g (Mat.)h(Inst.)g(Steklo)n(v.)f(\(LOMI\))g Fb(101)g FB(\(1981\),)g (101{110,)d(207.)-180 3882 y([L2])41 b(G.)28 b(Lusztig,)f Fe(Intr)l(o)l(duction)i(to)h(quantum)f(gr)l(oups)p FB(,)f(Birkh\177)-42 b(auser,)26 b(1993.)-180 4002 y([MiS])42 b(A.)29 b(Milinski)h(and)f (H-J.)g(Sc)n(hneider,)g Fe(Pointe)l(d)j(Inde)l(c)l(omp)l(osable)h(Hopf) f(A)n(lgebr)l(as)f(over)h(Coxeter)g(Gr)l(oups)p FB(,)e(Con)n(temp.)f (Math.)-9 4121 y Fb(267)e FB(\(2000\),)f(pp.)i(215{236.)-180 4241 y([M])49 b(S.)28 b(Mon)n(tgomery)-7 b(,)25 b Fe(Hopf)31 b(algebr)l(as)g(and)g(their)f(actions)g(on)g(rings)p FB(,)e(CBMS)g(Lecture)f(Notes)g(82,)g(Amer.)h(Math.)g(So)r(c.,)f(1993.) -180 4360 y([Mu])42 b(E.)27 b(M)r(\177)-44 b(uller,)28 b Fe(Some)h(topics)i(on)f(F)-6 b(r)l(ob)l(enius-Lusztig)29 b(kernels,)i(I)p FB(,)c(J.)h(Algebra)e Fb(206)h FB(\(1998\),)g (624{658.)-180 4480 y([Re])42 b(N.)23 b(Reshetikhin,)i Fe(Multip)l(ar)l(ameter)i(quantum)d(gr)l(oups)i(and)h(twiste)l(d)f (quasitriangular)h(Hopf)f(algebr)l(as)p FB(,)g(Lett.)e(Math.)f(Ph)n (ys.)g Fb(2)p FB(0,)-9 4600 y(\(1990\),)j(pp.)i(331{335.)-180 4719 y([Ri])42 b(C.)28 b(Ringel,)f Fe(Hal)t(l)k(algebr)l(as)g(and)f (quantum)e(gr)l(oups)p FB(,)g(In)n(v)n(en)n(tiones)f(Math.)h Fb(101)e FB(\(1990\),)h(583{591.)-180 4839 y([Ro])41 b(M.)28 b(Rosso,)e Fe(Quantum)j(gr)l(oups)h(and)g(quantum)e(shu\017es)p FB(,)g(In)n(v)n(en)n(tiones)f(Math.)h Fb(133)e FB(\(1998\),)h(399{416.) -180 4958 y([Sk])42 b(E.)28 b(K.)h(Skly)n(anin,)60 b Fe(Some)31 b(algebr)l(aic)i(structur)l(es)c(c)l(onne)l(cte)l(d)h(with)i (the)f(Y)-6 b(ang-Baxter)30 b(e)l(quation)p FB(,)g(F)-7 b(unctional)29 b(Anal.)g(Appl.)g Fb(16)-9 5078 y FB(\(1982\),)d(no.)h (4,)h(263{270)c(\(1983\).)-180 5197 y([Sw])42 b(M.E.)27 b(Sw)n(eedler,)g Fe(Hopf)k(algebr)l(as)p FB(,)e(Benjamin,)f(New)f(Y)-7 b(ork,)27 b(1969.)-180 5317 y([T])65 b(M.)27 b(T)-7 b(ak)n(euc)n(hi,)57 b Fe(The)31 b(c)l(or)l(adic)l(al)g(\014ltr)l(ation)f(for)g(the)g (quantum)f(algebr)l(a)i Fd(U)9 b FB(,)28 b(preprin)n(t)f(\(1994\).)p eop %%Page: 21 21 21 20 bop 1010 0 a Fp(A)33 b(CHARA)n(CTERIZA)-6 b(TION)31 b(OF)i(QUANTUM)f(GR)n(OUPS)1112 b(21)-180 203 y FB([W])42 b(S.)32 b(L.)g(W)-7 b(orono)n(wicz,)p Fe(T)h(annaka-Kr)l(e)e(\025)-34 b(\020n)32 b(duality)j(for)g(c)l(omp)l(act)f(matrix)g(pseudo)l(gr)l (oups.)h(Twiste)l(d)f FB(SU)q(\()p Fd(N)9 b FB(\))34 b Fe(gr)l(oups)p FB(,)f(In)n(v)n(en)n(tiones)-9 323 y(Math.)27 b Fb(93)h FB(\(1988\),)e(35{76.)-80 547 y FA(F)-10 b(a)n(cul)k(t)g(ad) 34 b(de)g(Ma)-6 b(tem)754 540 y(\023)751 547 y(atica,)35 b(Astr)n(onom)1450 540 y(\023)1460 547 y(\020a)e(y)h(F)1703 540 y(\023)1713 547 y(\020sica,)g(Universid)n(ad)f(Na)n(cional)g(de)h (C)3124 540 y(\023)3121 547 y(ordoba,)f(\(5000\))h(Ciud)n(ad)-180 666 y(Universit)-6 b(aria,)31 b(C)520 659 y(\023)517 666 y(ordoba,)g(Ar)n(gentina)-80 786 y Fe(E-mail)f(addr)l(ess)7 b FB(:)38 b Fr(andrus@mate.uncor)o(.e)o(du)-80 989 y FA(Ma)-6 b(thema)g(tisches)26 b(Institut,)f(Universit)1426 982 y(\177)1423 989 y(at)48 b(M)1656 982 y(\177)1653 989 y(unchen,)26 b(Theresienstra\031e)i(39,)d(D-80333)f(M)3342 982 y(\177)3339 989 y(unchen,)h(Germany)-80 1109 y Fe(E-mail)30 b(addr)l(ess)7 b FB(:)38 b Fr(hanssch@rz.mathem)o(at)o(ik.)o(un)o(i-m)o (ue)o(nc)o(hen)o(.d)o(e)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF