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HALId:tel-00002033https://tel.
archives-ouvertes.
fr/tel-00002033Submittedon27Nov2002HALisamulti-disciplinaryopenaccessarchiveforthedepositanddisseminationofsci-entificresearchdocuments,whethertheyarepub-lishedornot.
ThedocumentsmaycomefromteachingandresearchinstitutionsinFranceorabroad,orfrompublicorprivateresearchcenters.
L'archiveouvertepluridisciplinaireHAL,estdestinéeaudéptetàladiffusiondedocumentsscientifiquesdeniveaurecherche,publiésounon,émanantdesétablissementsd'enseignementetderecherchefranaisouétrangers,deslaboratoirespublicsouprivés.
CatégoriesdérivéesdeblocsàdéfautnonabéliendeGL(2,q)BertrandGonardTocitethisversion:BertrandGonard.
CatégoriesdérivéesdeblocsàdéfautnonabéliendeGL(2,q).
Mathématiques[math].
UniversitéParis-Diderot-ParisVII,2002.
Franais.
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7@'%&$ccd43i%l7@u)1F7@R&cd32GWQ5kcd'02Fm')1s!
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7@'%&$ccd'%l7@F2uX02Rl7@%Ecdd02jV"%&"02cd"'Rl77@%E(T,B)cd'gd'f7@92R&7@FWeiTuX)102A32p"dRWG32Gx32VpF2%r7@WG=NG(T)/CG(T)xcd'f365k)13i)iWDHFFQ)1'edf)1FV"R&V"!
#"F'U'%EBD%l7@R`"'sdf)1FV"R&V"!
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(92R&I32cdA)1%EFD'dpsicdr7@F32$P71$"02FI365k"FD'("0iscd'47@2j"R&V')132GW`HFCA)XdTw=(γwT)F.
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7@'%&$ccd3i%l7@u)1F7@R&cdy32GxTD0Q#R{5k)1F7@2A"RER&B"&'¨D25S Gxr"'(R&df)10QduX)102jTsx"F2u"FQ3iV7@γβ00βq"'7@2j"R&V"&'¨2¤&§EYE¨$$7@scd'rR{5kV"R&V"!
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#)12PQF*q*F*qxQ"'Tscd'32$7@3i%EF7@Rq21xi%&d)1!
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icdr$7@f71$"'q"cdr%EVc3i0Q$"'%E92R&cd432Tsd)1FD'47@R&)1dR&cdωij)102i=0.
.
.
q22WQxd)1%E'θR&$7@f71$"'q"cdH32F*q32VpF2%7@θ(α)=ξW2icd$7@f71$"'q"cd432Ted)1FD'47@R&)1drR&cdθ(i,j)xij)102i,j=0.
.
.
q2x32VpF2%&d7@θ(i,j):x00y→θi(x)θj(y).
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iUkWdj(kSVUj!
kXWqjGHFA)XdfHe=NG(Te)Wrxd)1%E'WeR&d)10Qdh{uX)102A#365k)13i)b"F2u"FQ3iV7@˙s=0110WHFI7He=TeWex2)'abR{5871$"'%&)1FC32Wed02Tecd'32)1F2FQVc7@˙sx00y˙s1=y00x.
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#"!
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kWdjQ¤qSWdjGjVEj(iUUkISVUUedhkj!
iUkxD%=px132)1FQ$d%3i%EBd%&dqxX7@R&)1deR&cdhad)10Qdh{uX)102jcde32xDDR&)F632Gdf)1F'eR&cdd)10Qdh{uX)102Acds$c)1F102uX0QVcds7@0wuX)102je32e!
7@'%&$ccd32(Rl7~)1!
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#)1F'Vcg3Q7@FQds$c$71d`AGW`SU)10QV7)192'"FD0p32cdH%&df)1'ad2%&cd$akSx81tc&tx"'WAHd027@!
77$c)1FQd'02%E'H32cdVc02%EBX7@R&"FQ$ccd32V"%EBVccdHj)102R&(uX)102ASL2(q)$aHc&tWxD%3i%EBd%&dq1xw7@R&)1dTe$c)1F'%&"FD'#02Fhad)10Qdh{uX)102jm!
7sd%E!
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#"!
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7@%EF'"F7@F'0Q=2"'D0Qqcd'%E!
g7@%EWHFC7y7@R&)1dq1=2au"'q+1=2bv7cBc$u"'v%E!
g7@%EdxX"'fR{5k)13i36502Fhad)10Qdh{uX)102jr324xDDR&)F632Gcd'22a+bWdxd"R&)1FmRl7$c)1F2uX0Q"FQ$cs32q!
#)d3i02R&)4QxDR{502F32cdU"F'%&"da"'bcd'V"u7@Re%"'sR{587@02'gcd'dFD'(d02jV"%&"02(%Wjicd(d)10Qdh{uX)102jcdPe"'Psd)1F'r365k)13icdjc$"'%~22a"'2a+bx27@%EFQd%AR{502F32$ccd32"0ismuX)102Acdrcd'365%EFQ3i%&$c)3Q7@FQdr02FCd)10Qdh{uX)102j32(xDdR&)(6¨32GWxD%qcd'$c)1F2uX0C%!
#)d3i02R&)4Qx27@R&)1db=1xi"'02Fdf)10Qdh{uX)102As32xDdR&)(632Gcd'Se=PeWeWQYaR6F5kcd'r71d47@9AV"RE%&"FWxd)1%E'He=NG(Se)WAHFC)192'%&"F'He=x00xαn,0xxαn0x∈F*q,n=0.
.
.
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#"FD'FQ)1Fih{'%EBd%l7@RH32C2d02Cq1*C2acd'32)1F2FQVcb7@(x,y)→(xy,y1)$"F02'%ERE%&df7@F'R{5%EF1c$"'%&)1F$7@FQ)1F2%&0QC2a→Cq1&tWrxdcd$7@f71$"'q"cd%EVc3i0Q$"'%E92R&cdd)1F'432)1F2FQVcd47@rRl7'f7@92R&SsW%8y7@u)32WxD%qcd'$c)1F2uX0C!
#)d3i02R&)4QxQ7@R&)1da=1"'r02Fbd)10Qdh{uX)102j32(xDDR&)F632Gcd'Ss=PsWsW2YaR6F5kcd'471d47@9AV"RE%&"FCFQ)1Fb2RE0QdWxd)1%E'Hs=NG(Ss)γWHFC)192'%&"F'Hs=βn00βqn,0βnβqn0n=0.
.
.
2b(q1)1.
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#)12P2%&d!
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#"F'd%qcd'r%E!
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"1=2§q8HFbd022j)Xd32)1FQ$D0Q=2"'4D0Qqcd'r%E!
g7@%EWi$7@3i%EF7@RT32Gcd'|GL2(q)|=(q1)2q(q+1)=22a+bqu2v,)39GL2(q)32)1FQ$$c"RE02%}32PSL2(q)cd'|PSL2(q)|=12(q1)q(q+1)=2a+b1quv.
ueF$c)1FQdVcD0Q"FQ$cod%q≡±3mod87@R&)1dbR&cd)had)10Qdh{uX)102jcdI32xDDR&)F632PSL2(q)d)1FD'365k)13i4QxA"'%ER&dd)1FD's32)1FQ$g7@9jV"RE%&"FQdWji"02ds%E!
7@ucdsVc$"%E2)d0Qcd3Q7@FQdSL2(q)d)1FD'32cdrd)10Qdh{uX)102jcd32(xDDR&)F632SL2(q)W2YaR&dFQsd)1FD'r2RE0Qd47@9jVthRE%&"FQdxd!
7@%&dFQ)10Qd7@RER&)1FQdrB)1%ErD0QR&"02UFQ)1!
7@RE%&d7@'"0243Q7@FQdG$c)1F'¨1R&Rl7~0Qd%&)1F32cd)hadf)10Qdh{uX)102AcdH32GW&)10QdgB")1FQdm"FQd02%E'bD0Q7@$c)1F'Xxd%q≡±1(mod8)xf7@R&)1dm7@0Q$"02Fd)10Qdh{uX)102A4R&)D$7@R`FQ4$c)1F'¨1R&HRl7~0Qd%&)1FWi}732VpF2%E'%&)1F32Rl7FQ)1'%&)1Fm324$c)1FD'¨1R&32Rl7~0Qd%&)1FpuX023Q7@FQd4R{587@F2FQtsi(v$32VpF2%E'%&)1FwveW0)iW%&tWDFEEGDdkq≡±3(mod8)HFyd022j)Xdw32)1FQ$fD0Qq≡±3(mod8)W1xd)1%E'P02F)had)10Qdh{uX)102jf32xDDR&)F632SL2(q)"'H=NG(P)d)1FFQ)1!
7@RE%&df7@'"023Q7@FQdGWxD%q≡5(mod8)xX)1Fg$fPQ)1%&d%E'eA)102PR&d)10Qdh{uX)102jU32PeWe$c)1F'"F7@F'R&cdyV"R&V"!
#"F'd32#Rl7~)1!
#x00x1"'0xx10WrxD%q≡3(mod8)xr)1F$fPQ)1%&d%E'j)102PR&d)10Qdh{uX)102j32PsWs32VpF2%T32s!
7@F2%&q"y7@F7@R&)1uX0QXx$X5kcd'hiTcd4d'0Q$"'02cdH32P"'32Hd)1FD'432)1F2FQVccd7@rRl7g2)12%&V"'Vd02%EBX7@F'R`!
RTG02$9E&')1&'¨§$9@)R@PQ8NSL2(q)(P)Q8C3EH(Q8C3)Cq1¨"DG($GFRS0HFCdfV"7@sR&cd$71dq≡5(mod8)"'q≡3(mod8)WDq≡5(mod8)HFmBV"%p~71$"%ER&"!
#"FD'r0QPcd'U%&d)1!
#)12PQs7@0uX)102jHD07@'"F2%&)1F2%&D0Qs`V"R&V"!
#"FD'dH"Fj)Xdf7@F'hI=α00α"'hJ=0110xQ202%&dhK=hIhJ=0αα0WvHR&)1dPcd'H"F2u"FQ3iVy7@hI"'hJx$ccds32"0isCV"R&V"!
#"F'dd)1FD'365k)13i4Qx`R&"02d$7@VcdHd)1F'4V"u7@0is6x2"'hIhJh1I=h1JWHFI$7@R&$"02R&"FQd02%E'D0QH=αi100αj,αi01αj0,αi1αjαkαj+ki=0.
.
.
q2,j,k=0.
.
.
3.
HFA)XdA=α+1211αα`T$X5kcd'e02FV"R&V"!
#"FD'y365k)13i"'y3232V"'"!
g%EF7@F'%W`HFC!
#)1F'(D0QsR&$7@3i%EF7@Rr32NSL2(q)(P)cd'24x32)1FQ$0QNSL2(q)(P)Q8C3W2iw5871$"'%&)1FI32Ad02Q8cd'32)1F2FQVc7@AhIA2=hJxAhJA2=hKW¨=2qHFj)Xde"FQd02%E'B=α01αα1x)'aα0cd'602FQwf71$"%EFQf32α/2W@q})1027T#!
#"0Qα0cd'492%&"FIV"R&V"!
#"FD'32F*q%ER~7@02'd5871dd02"0Q)gF5kcd'H71d402Fw$7@VXx`)1FA"02'R&gBV"%p"y3Q7@FQdaxd()c`Q)bcd'02Fo$7@V#3Q7@FQdFpd%w"'(d"02R&"!
#"FD'p≡±1mod8xr$cD02%d5kV"'"FQ3~71$"%ER&"!
#"FD'#q=pn"FdV"7@f7@F'yR&cde$71dn7@%Ey"'n%E!
g7@%EWicdBX7@R&"02d2)12cdg321αα1d)1F'1±αxrR&32V"'"!
g%EF7@F'32Bcd'αx32)1FQ$Bcd'm365k)13i(q1)"'mR&CuX)102j05%ERs"F2u"FQ3icd'365%EF'"dc$"'%&)1F'%EBD%l7@R&C7Bc$SL2(q)WfuwFFQ)1'f7@F'Cq1$c"RE02%nha$"%s)1F732)1FQ$b02F%&d)1!
#)12P2%&d!
#H(Q8C3)Cq1WDq≡3(mod8)HFb$7@R&$"02R&(D0QHγ=αiβj100β2j,αiβj01β2j0,αiβj+k11β2j+1β2k+1β2(j+k1)i=0.
.
.
q2,j,k=0.
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55SU"2Vcdf"F'f7@F'!
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Hn(SE)SHn(E)¨"DG($GFRS0xd)1%E'dRl73i%¨6V""F'%&"RER&32EWdHF$c)1FQd%&32q"4Rl7(d02%E'tsQ71$"'0→kerdn→En→imdn→0.
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g!
#Scd'r2Rl7@'d02RRl7d02%E'0→Skerdn→SEn→Simdn→0cd'H')101)102dtsQ71$"'XW`YR}cd'$"Rl7@%EHD0QSimdn=im(1Sdn)x32)1FQ$y)1Fw702F%&d)1!
#)12P2%&d!
#Skerdnker(1Sdn)WHFI$c)1FQd%&32q""FQd02%E'Rl7#d02%E'ts271$"'0→imdn1→kerdn→Hn(E)→0.
tss!
#"!
#XxSV"'f7@FD'2Rl7@'Xx)1FC7y02FQ(d02%E'tsQ71$"'0→im(1Sdn1)→Skerdn→SHn(E)→0.
39'H)1FI7Skerdn=ker1Sdn"'r02FQ(d02%E'ts271$"'0→im(1Sdn1)→ker(1Sdn)→Hn(SE)→0365k)'abR{5%&d)1!
#)12P2%&d!
#SHn(E)Hn(SE)WgH7@2j"R&)1FQdrRl7$c)1FQd'0Q$"'%&)1Fwd02%EB17@FD'$B)1%E7@4ts2"!
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g2R&tsi32cd!
#)12P2%&d!
#cdw32C3Q7@FQdD5SF§&')5PHomA(C,D)2HomA(C,D)n=i∈ZHomA(Ci,Di+n),d(f)=dDf(1)nfdCpourtoutf∈HomA(C,D)n.
HFFQ)1'EndA(C)=HomA(C,C)W}qr)102g')102'n)1F7IRl7b2)12%&V"'Vd02%nhB17@FD'1`Hn(HomA(C,D))=HomH(A)(C,D[n]).
!
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8Q&8¨@V§F§&')&'E!
'Y020#857&'¨@46B$9E&')1&'¨§$9@)RSRHomH(A)(C,D)→HomH(SRA)(SRC,SRD).
¨D(G($GFRS0ty587@2qcdakSUd%{x`$fP7@W6Yx)ixAF%2ixA2)1W%3%cj)102H')102'Rh!
#)D3i02R&X324'adApF2%`"'U')102'Rh{!
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iw5%E!
7@u47@$c"'f%&df)1!
#)12P2%&d!
#s32λfcd'R{587@22RE%&$7@'%&)1Fb02%jx∈SX71dd)d$"%&λf(x)WxD%}32e2RE0QdX"'Yd)1F's32cdGh{!
#)d3i02R&cdxj7@R&)1dR&Rh{!
#)d3i02R&HomR(X,Y)cd'!
(02F2%436502FQC71$"'%&)1F32G"FA)Xdf7@FD'#j)102g∈Gx∈HomR(X,Y)"'x∈X`(g)(x)=g((g1x)).
HF7m7@R&)1dHomRG(X,Y)=(HomR(X,Y))Gx$¤§HomRG(X,Y)cd'sR{5k"Fihd"!
(92R&32cdA)1%EFD'dps2cd32HomR(X,Y)j)1024$c"''(71$"'%&)1FWts#1F7HomSG(SX,SY)=(HomS(SX,SY))GxT"'R{5%&d)1!
#)12P2%&d!
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g7@'%E92R&7cBc$$c"''471$"'%&)1FWYaR2%EFQ3i02%E'w02Fg%&df)1!
#)12P2%&d!
#τ:SHomRG(X,Y)→HomSG(SX,SY).
23xD%X"'Ydf)1F'432cdAh{!
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#)12P2%&d!
#1`τ:SHomA(X,Y)→HomSA(SX,SY).
U)1FQd%&32V")1FQd!
7@%EFD'"F7@F'32"0is$c)1!
g2R&ts2cd32Ah{!
#)d3i02R&cdC"'Dx)'aCcd'9j)1FQVXx`$c)1!
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g2R&ts2HomA(C,D)"'dS$c"RER&3i0C$c)1!
g2R&ts2HomSA(SC,SD)WU)1!
g!
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#)12P2%&d!
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#)12P2%&d!
#S(HomA(C,D))n→(HomSA(SC,SD))nWDHFBV"%p0Qτ(1SdR)=dSτx32)1FQ$#D0Qτ32VpF2%E'e02Fp%&d)1!
#)12P2%&d!
#32$c)1!
g2R&ts2cdWU"RE02%nha$"%}%EFQ3i02%E'432)1FQ$02F%&d)1!
#)12P2%&d!
#("FbPQ)1!
#)1R&)1uX%&32(32"uXV2H0(τ):H0(S(HomA(C,D)))→H0(HomSA(SC,SD))=HomH(SA)(SC,SD).
iTR&"!
g!
#W0)iW4#FQ)10Qd71dd02D0QH0(SHomA(C,D))SH0(HomA(C,D)),32)1FQ$)1Fw7yR{5%&d)1!
#)12P2%&d!
#(32Vcd%EVXW!
RTGUBO46B!
'(V§!
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g2RE%p"WrHFo77@R&)1ddn1d02c$Cn2)@c$"'%~x32)1FQ$%ERftsi%&d'02F!
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3i(!
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#)12P2%&d!
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g%ERER&32w!
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g!
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#"F'R&cd3i07@0isyd02k7@02FQV"')1%ER&r"Fy971d'&tWHFg7H9jcd)1%EFg32fR{5PDDj)1'PQqcdHi(kC)=0A)102r!
#)1FD'"HD0QHi(C)=0`Q$c)1!
g!
#kcd'r02FI$c)1Qd4)1FC7HomH(k)(kC[i],k)=Homk(Hi(kC),k)=Hi(kC).
ty587@02'7@'HomH(k)(kC[i],k)=Hi(Homk(kC,k))=Hi(kC)32)1FQ$m$c)1!
g!
#Hi(C)cd'02Fd)10Qdhacd71$c32Hi(kC)xr)1F7Hi(C)=0A)102r')102'4"FD'%&"iWHF)192'%&"FD'32CRl77c)1F0QC2Vc$cVc32"!
g!
#"F'02FQ~7@!
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#"F'df"FycdAc$"'f7@FD'rRl7Hq"uXR&32d%EuXFQcdr32v4)XdA@c02R{xF!
akv(9QxW%c`2d%f"'gdf)1F'432"0isb7@22RE%&$7@'%&)1FQd4"'x"'y32"0isV"R&V"!
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#)1uq"FQ(3232"uXVi"'xPQ)1!
#)1uq"FQe3232"uXVj7@R&)1d(fg)(xy)=(1)ijf(x)g(y).
iw587@22RE%&$7@'%&)1Fm1cd'7@2j"R&Vc#3i%¨6V""F'%&"RER&32Ax6"'R{587@22RE%&$7@'%&)1Fm2cd'7@2A"R&Vc!
(02RE'%E2RE%&$7@'%&)1FWueRER&scd'U32)1FQ$4y71ddf)D$"%l7@'%EBsePQ)1!
#)1')12%&s2qcd|fxD"'r$c"''PQ)1!
#)1')12%&(cd'rR{587@22RE%&$7@'%&)1Fm3`···GG(A3)idi(A3)GGm2(1m2m21)(A3)i+1m3vvlllllllllllllllm2(1m2m21)GG······GGAim1GGAi+1GG···xD%mn=0j)102}')102'n≥37@R&)1dAcd'T02FQth7@REuq"92XWXxD%m1=0x17@R&)1dAcd'e02FQH7@REuq"924uXf713i0QVc!
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(02Rl7@'%&)1Fw3i0bVcd02RE'f7@'`§§HR8$P46E&84'¨&'42#'5S&2GQ46&'4'¨&'42PEg465SE)1E2GY54(Qg≤P¤5S&'¨@$5'$9Y2@&'4'¨&'4@L1.
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g2RE%p$7@'%&)1FIuX1$c(7@0'PQVc)1q"!
#(365kvHREA"%EFW¨"RGFRSBG4'¨&'4$H46E&'4@'¨&'42Gp46&')RQ¨28$4GHF§5P5S!
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4@$&'B2@pYE&'4@'¨&'4@2G@$%`3`HF§&8%$E46p"&'4'¨&'412#'5S&P2G¤$Q4p"&'4@8¨W&'42PEg46E5S)R2GY54GgQ≤H!
'57&8¨g∈HCG(Q)i}72)12%&V"'V(d02%EBX7@F'(cd'$c)1FQdVcD0Q"FQ$c32Rl7y2)1j)Xd%E'%&)1FakPTx$4'W08c`!
RTGBBG46'¨&'4($Ep46R&8)1QE¨E¨P461&'4@'¨&'4C2#'57&2GEH461&'4'¨&'42GF§&'Y!
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#"FD'32G'"RQD0QgQ≤HWxd)1%E'P02Fphad)10Qdh{uX)102A324xDdR&)(632H$c)1FD'"F7@F'gQWYRTtsi%&d'h∈H'"Rr0QgQ≤hPx$9§h1gQ≤PWAU)1!
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LnR&cdeuX)102jcdR&"024$c)1cdA)1FQ3Q7@FD'Wqr)1024')102'i)1FbFQ)1'QiRl7d)102$c32iWHF7Qi≤Li≤Pxr"'icd'y%EFQ3i02%E'7@02FV"R&V"!
#"FD'#32NG(Li)x32)1FQ$7@w02F#V"R&V"!
#"FD'f32NH(Li)CG(Li)36587@2qcdwR{5PDDj)1'PQqcd(iii)WDU)1!
g!
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#"F'e32HW6qr7@$c)1!
gj)Xd%E'%&)1Fxcd's%EFQ3i02%E'7@s02FpV"R&V"!
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#32SU02FQd%&32R`§§HRSBUG46'¨&'4($P46p"&'4'¨&'4C2#5S&2GEH=NG(P)&'&8¨@)1!
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g!
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#"F'$"R&)Xd432$7@f71$"'V"%&d'%&D0Qp%E!
g7@%EXxqcd'402FQs202%&ddf7@FQ$c32pxβcd'r02FuV"FQV"f7@'"02H32F*q23Q7@FQdFxα=βq+132)1FQ$αcd'r02FCuV"FQV"f7@'"02H32F*qxaxbxu"'vd)1FD'R&cd"F'%&"dH'"R&d4D0Qq1=2auxq+1=2bvxu"'vV"'f7@FD'%E!
g7@%Edx(K,O,k)cd'(02Fdid'q"!
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#)d3i02Rl7@%EXxOV"'f7@FD'd022A)XdV71dd@uX)XdyA)102')10QdrR&cdruX)102jcd4"F2Vcdf"FQ$cXxζcd'r02FQf71$"%EFQ32R{502F2%E'V365k)13iq213Q7@FQdOxξ=ζq+1WPSL2(q)HF02'%ERE%&db3Q7@FQd#$c"''7@'%&bR{587@'%&$"R&b32bSU02DP7@3i'XakSU0cxeD02%32)1F2FQR&cd$7@f71$"'q"cd!
#)D3i02Rl7@%EcdU%EVc3i0Q$"'%E92R&cd32cduX)102AcdPSL2(q)"Fm')102'$7@f71$"'V"%&dh'%&0QXW¨EGDFEGDdkq≡1(mod4)iT7e'f7@92R&SsW%32)1F2FQsR&cdr$7@f71$"'q"cd%EVc3i0Q$"'%E92R&cd32cduX)102AcdPSL2(q)WdiTcdV"R&V"!
#"F'd4df)1F'"2Vcd"FD'Vcd47@r02FI32R&"02d47@F'Vc$cVc32"FD'ds3Q7@FQdSL2(q)W%`'%('2i}7y'f7@92R&SsW0)y32)1F2FQsRl7ecd1Fb32cdr$7@f71$"'q"cdr%EVc3i0Q$"'%E92R&cdH32PSL2(q)7@0is)i5haV"R&V"!
#"F'dW6iT7m'f7@92R&SsW32)1F2FQR&cds$7@f71$"'q"cd!
#)D3i02Rl7@%Ecds%EVc3i0Q$"'%E92R&cd32PSL2(q)Wi}7!
7@'%&$c(3232Vc$c)1!
gj)Xd%E'%&)1FIcd'`11112···111111···1WWW11WWW11WWW1.
.
.
1WWW11WWW1.
iTcdH92R&)d$cd1WWW11WWW1d)1FD'32('f7@%ERER&u12*(u1)xA%ER&d7@27@f7@%&ddf"F'2a2~)1%&d$P71$"02FxQ7@%EFQd%jR&)e7@27@f7&'2a21~)1%&dWdis92R&)D$1WWW1pF7@R6cd'32'f7@%ERER&q14*q14WQiT7y!
7@'%&$ce32(7@'f7@FIcd'`2a2a12a12a12a2+12a22a12a22a2+12a1WWW2a11WWW1.
r7@92R&7@0I32cdχ(g)|Cl(g)|χ(1)(mod2)`11000011000011000011ξin+ξin000100ζ4in+ζ4in11iTcd$7@f71$"'q"cd3i092R&)d$2%EFQ$"%E7@Rjd)1FD'32)1FQ$HR&cdf$7@f71$"'q"cd0x0x1x1x"'R&cdλuq1λuA)102λ=1.
.
.
2a21W¨EGDVEFkq≡3(mod4)i}7'f7@92R&oSsW432)1F2FQoR&cdC$7@f71$"'q"cdw%EVc3i0Q$"'%E92R&cdw32PSL2(q)d%q≡3(mod4)W¨PSL2(q)%('$%¤`SsW%7@f71$"'q"cd%EVc3i0Q$"'%E92R&cd32PSL2(q)xq≡1(mod4)1001αn00αnn=q14αn00αnn=1.
.
.
q54γβ(q1)n00β(1q)nn=1.
.
.
q1411011α01q(q+1)2q(q+1)q(q1)q212q21201111110q11100εε=±q+12(1)q14(1)n012(1+ε√q)12(1ε√q)iq1ii=1.
.
.
q54q+1ξiq14+ξiq14ξin+ξin011ψ(q1)ii=1.
.
.
q14q100ζ2(q1)inζ2(1q)in11¤SsW0)gHcd1FQd47@0is2haV"R&V"!
#"F'd21001αn00αnn=1.
.
.
u12γβun00βunn=1.
.
.
q1411011α010111110q1100εq+121012(1+ε√q)12(1ε√q)iq1iq+1ξ2a1in+ξ2a1in011ψ(q1)iq10ζ2(q1)inζ2(1q)in11¤`SsW7@f71$"'q"cd!
#)d3i02Rl7@%Ecd%EVc3i0Q$"'%E92R&cd32PSL2(q)xq≡1(mod4)21001αn00αnn=1.
.
.
u12γβun00βunn=1.
.
.
q1411011α01σ011111σ+q120112(1+√q)12(1√q)σq120112(1√q)12(1+√q)σii=1.
.
.
u12q+1ξ2a1in+ξ2a1in011τii=1.
.
.
q14q10ζ2(q1)inζ2(1q)in11&)1'`α=α2a1xβ=β2aWi}7o'f7@92R&SsW0832)1F2FQIR&"02dcd1FQd7@0is2haV"R&V"!
#"FD'dxr"'mRl7o'f7@92R&SsW0932)1F2FQR&cd4$7@f71$"'q"cd4!
#)d3i02Rl7@%Ecd%EVc3i0Q$"'%E92R&cd32PSL2(q)d%q≡3(mod4)Wi}7!
7@'%&$c(3232Vc$c)1!
gj)Xd%E'%&)1FIcd'`11···111111···1WWW11WWW11WWW1.
.
.
1WWW11WWW1.
iTcd92R&)D$cd1WWW11WWW1d)1FD'32'f7@%ERER&v12*(v1)xj%ER&d7@27@f7@%&dfd"F'2b2~)1%&df$fP71$"02FWi492R&)D$1WWW1pF7@Rcd'32r'f7@%ERER&q34*q34WiT7!
7@'%&$cH32H7@'f7@Fcd'`21112b2+12b212b22b2+12b1WWW2b11WWW1.
r7@92R&7@0I32cdχ(g)|Cl(g)|χ(1)(mod2)`101000101000101000101ζ(q1)in+ζ(1q)in001ξin+ξin0011iTcd$7@f71$"'q"cd3i092R&)d$2%EFQ$"%E7@Rjd)1FD'U32)1FQ$4R&cd$7@f71$"'q"cd0x0xψ1xψ1x"'R&cdψλ(q1)vj)102λ=1.
.
.
2b21WPGL2(q)i}7'f7@92R&HSW32)1F2FQ4R&cdU$7@f71$"'q"cdU%EVc3i0Q$"'%E92R&cd32PGL2(q)WDicdUV"R&V"!
#"F'dd)1FD'}"2Vcdf"F'Vcd7@r02Fy32fR&"02d7@FD'Vc$cVc32"F'dw3Q7@FQdGL2(q)W@iT7'f7@92R&USsW0`432)1F2FQR&"02d4cd1FQdH7@0is2haV"R&V"!
#"F'dWPGL2(q)%('X¤`SsW47@f71$"'q"cd%EVc3i0Q$"'%E92R&cd32PSL2(q)xq≡3(mod4)1001αn00αnn=1.
.
.
q34γβ(q1)n00β(1q)nn=q+14γβ(q1)n00β(1q)nn=1.
.
.
q3411011101q(q+1)q(q1)2q(q1)q212q21201111110q11100ψεε=±q120(1)q34(1)n1+ε√q21ε√q2ψ(q1)ii=1.
.
.
q34q10ζq214iζ1q24iζ(q1)inζ(1q)in11iq1ii=1.
.
.
q34q+1ξin+ξin0011¤SsW08gHcd1FQd47@0is2haV"R&V"!
#"F'd21001αn00αnn=1.
.
.
q34γβun00βunn=1.
.
.
v12110111010111110q1100ψεq120112(1+ε√q)12(1ε√q)ψ(q1)iq10ζ2buiζ2bui11iq1iq+1ξin+ξin011¤`SsW097@f71$"'q"cd!
#)d3i02Rl7@%Ecd%EVc3i0Q$"'%E92R&cd32PSL2(q)xq≡3(mod4)21001αn00αnn=1.
.
.
q34γβun00βunn=1.
.
.
v1211011101σ011111σ+q120112(1+√q)12(1√q)σq120112(1√q)12(1+√q)τii=1.
.
.
v12q10ζ2buiζ2bui11σii=1.
.
.
q34q+1ξin+ξin011&)1'`β=β2bW%('4¤¤`SsW7@f71$"'q"cdH%EVc3i0Q$"'%E92R&cd432PGL2(q)10011001100αnn=1.
.
.
q32βq+12γ1001γβn00βqnn=1.
.
.
q1211011q(q+1)2q(q+1)q(q1)2q(q1)q210111111q121(1)q12(1)n(1)q+12(1)n10q11110q12q(1)q12(1)n(1)q12(1)n0iq1ii=1.
.
.
q32q+12(1)iξin+ξin001ψ(q1)ii=1.
.
.
q12q1002(1)iζ(q1)inζ(q1)in1¤¤`SsW0`g4cd1FQdH7@0is2haV"R&V"!
#"FD'd21001100αnn=1.
.
.
u12γβn00βqnn=1.
.
.
v1211010,q1211110,q12q110iq1iq+1ξ2ain+ξ2ain01ψ(q1)iq10ζ2a+b(q1)inζ2a+b(q1)in1¤`SW'7@f71$"'q"cd!
#)d3i02Rl7@%Ecd%EVc3i0Q$"'%E92R&cd32PGL2(q)xq≡1(mod4)21001100αnn=1.
.
.
u12γβn00βqnn=1.
.
.
v121101ρ01111ρ0q1021ρii=1.
.
.
u12q+1ξ2ain+ξ2ain01ρii=1.
.
.
q14q10ζ2a+b(q1)inζ2a+b(q1)in1&)1'1`α=α2axβ=β2a+bWPGL2(q)%('8¨E9EGDdkq≡1(mod4)}7@92R&7@0w32cdχ(g)|Cl(g)|χ(1)(mod2)`11000011000011000011000011ξin+ξin0001001ζ(q1)in+ζ(q1)in0icdm$7@f71$"'q"cdm3i092R&)d$b2%EFQ$"%E7@Rd)1F'm32)1FQ$0xq12x0xq12x"'R&cdiq1i'"R&dD0Qu|i$%ER&d4d)1F'H7@0CFQ)1!
(92(322a1+3&tW7@R&$"02RT32cd$7@f71$"'q"cdH!
#)D3i02Rl7@%Ecd4%EVc3i0Q$"'%E92R&cd`v42j"R&)1FQdρ0xρij)102i=1.
.
.
u12x@"'ρiA)102i=1.
.
.
q14R&cd}cd1FQd7@0is2haV"R&V"!
#"FD'dr32cd$7@f71$"'q"cdUcdjc$"'%~d0xiq1ix"'ψ(q1)iWiT7cd1F32$P71$"02FI32($ccd$7@f71$"'q"cdPSL2cd'r02FI$7@f71$"'q"!
#)d3i02Rl7@%E%EVc3i0Q$"'%E92R&Xx32)1FQ$%ER&dd)1FD'4"0isDh{EVc3i0Q$"'%E92R&cdWueF~7@%&df7@FD'R&$c)1!
g2'3i0FQ)1!
e9232$"Rl71ddcdU32$c)1F102u7@%&d)1F322haV"R&V"!
#"FD'd)1F$c)1FQd'f7@'wD05%ER!
7@FQ0Qw02F($7@f71$"'q"e!
#)d3i02Rl7@%Ew%EVc3i0Q$"'%E92R&XWvH2j"R&)1FQdh{R&ρ0Wi92R&)d$2%EFQ$"%E7@Rj$c)1F'%&"FD'47@0!
#)1%EFQdU32"0is$7@f71$"'q"cd!
#)d3i02Rl7@%EcdU%EVc3i0Q$"'%E92R&cd$7@f')10QdUdcd$7@f71$"'q"cdUFQHd)1F'U71df!
e02RE'%E2R&cd3i0$7@f71$"'q"'%EBD%l7@R{xD32)1FQ$ρ0cd'3Q7@FQdrR&92R&)d$s2%EFQ$"%E7@R{WU)1FQd%&32V")1FQdR&4$7@f71$"'q"H%EFQ3i02%E'32PSL2PGL27@σ+$)107@σ&tWdHFBdV"%pD05%ERTcd'3Q7@FQd4R&s92R&)D$s2%EFQ$"%E7@Rr32PGL2x232)1FQ$$c)1!
(92%EF7@%&d)1FwRE%EFQV7@%E($c)DT$"%&"FD'd"F'%&"dsj)Xd%E'%~d)10FD02R&d32ρ0"'32ρ0WHdf7cd1FoPSL2cd'σ++σx2$c(02%6%E!
gj)XdD0Qρ0=IndPGL2PSL2σ+WHF¨"F¨32Vc3i02%E'IRl7'f7@92R&pSsW'32cdI$7@f71$"'q"cdC!
#)d3i02Rl7@%Ecdb%EVc3i0Q$"'%E92R&cd32PGL2(q)j)102q≡1(mod4)x2202%&ddf7y!
7@'%&$ce3232Vc$c)1!
gA)Xd%E'%&)1F`11112···1111WWW11WWW11WWW1.
.
.
1WWW11WWW11WWW1.
icd92R&)D$cd1WWW11WWW1d)1F's32('f7@%ERER&u12*(u1)xA%ER&d7@27@f7@%&dd"F'2a1~)1%&dr$fP71$"02FWi92R&)d$1WWW11WWW1pF7@RTcd'32'f7@%ERER&q14*q12W%('9i}7!
7@'%&$c(32(7@'f7@FCcd'`2a+12a2a2a1+12aWWW2a2WWW2.
xD%q≡5(mod8)xR&cd$7@f71$"'q"cd(3i092R&)D$2%EFQ$"%E7@Rd)1F'0xq12x0"'u3uW`xdcdr!
7@'%&$ccdH3232Vc$c)1!
gA)Xd%E'%&)1Fw"'32e7@'f7@FCd)1FD'11112111et8443.
$SsW%&¨E7EFkq≡3(mod4)r7@92R&7@0I32cdχ(g)|Cl(g)|χ(1)(mod2)`10010010010010010010010011ξin+ξin0001001ζ(q1)in+ζ(q1)in0iTcd$7@f71$"'q"cd43Q7@FQdrR&s92R&)d$2%EFQ$"%E7@RTd)1FD'0xq12x0"'UR&cdψ(q1)i'"R&dD0Qv|i$%ERdf)1F'H7@0bFQ)1!
e92(322b1+3&tWiTsf7@%&d)1F2FQ"!
#"F'02'%ERE%&dfV3Q7@FQdR&s$71dq≡1(mod4)j"7@0Qdd%6365k)19ih'"F2%ERl7g'f7@92R&SsW%232cd$7@f71$"'q"cd4!
#)d3i02Rl7@%Ecd%EVc3i0Q$"'%E92R&cdWxi7g!
7@'%&$c3232Vc$c)1!
gj)Xd%E'%&)1FCcd'Rl7d02%EB17@FD'1`1111···1111WWW11WWW11WWW11WWW11WWW1.
.
.
1WWW1.
iTH2"!
g%&"r92R&)d$1WWW11WWW1cd'r32H'f7@%ERER&q34*q32xDR&cdU92R&)D$cd1WWW11WWW1d02%EBX7@F'dHd)1F'H32s'f7@%ERER&v12*(v1)x2%ER&dd)1FD'H7@0FQ)1!
(92e322b1WSL2(q)%('iT7!
7@'%&$c32y7@'f7@FCcd'`4222b1+12WWW22bWWW2b.
xD%q≡3(mod8)xiR&cd$7@f71$"'q"cd3Q7@FQdrR&92R&)d$s2%EFQ$"%E7@RTd)1FD'0xq12x0"'ψ(q1)vWxdcdr!
7@'%&$ccd3232Vc$c)1!
gj)Xd%E'%&)1FI"'32e7@'f7@FId)1F'1111111et4223.
$SsW0)&¨SL2(q)icd$7@f71$"'q"cdH%EVc3i0Q$"'%E92R&cd432SL2(q)d)1FD'432)1F2FQVcd7@4Rl7y'f7@92R&SsW%3%W}7@92R&7@0w32cdχ(g)|Cl(g)|χ(1)(mod2)`100000010000001ξin+ξin0q12q12q12q1210ζin+ζinq+12q+12q+12q+1210000001000000icd$7@f71$"'q"cd4!
#)d3i02Rl7@%Ecd%EVc3i0Q$"'%E92R&cddf)1F'4R&cd4cd1FQds320xψ1"'ψ1WxD%q≡1(mod4)x2Rl7!
7@'%&$c(3232Vc$c)1!
gA)Xd%E'%&)1FCcd'112.
.
.
11111111111WWW11WWW11WWW1.
.
.
1WWW11WWW1.
icd92R&)D$cd1WWW11WWW1d)1F's32('f7@%ERER&u12*(u1)xA%ER&d7@27@f7@%&dd"F'2a1~)1%&d$P71$"02FxQ7@%EFQd%AR&)7@27@f7&'2a11~)1%&dWdi92R&)d$1WWW1pF7@Rjcd'32'f7@%ERER&v12*v12WiT7!
7@'%&$c32e7@'f7@FIcd'`¤SsW%27@f71$"'q"cdf!
#)D3i02Rl7@%Ecde%EVc3i0Q$"'%E92R&cdU32PGL2(q)xq≡3(mod4)21001100αnn=1.
.
.
u12γβn00βqnn=1.
.
.
v121101ρ01111ρ0q1021ρii=1.
.
.
q34q+1ξ2in+ξ2in01ρii=1.
.
.
v12q10ζ21+b(q1)inζ21+b(q1)in1¤SsW%3%§7@f71$"'q"cdH%EVc3i0Q$"'%E92R&cd32SL2(q)xq%E!
g7@%Eλ1001λ=±1αn00αnn=q32γβn00βnn=(q1)mm=1.
.
.
q12110111011α011α01q(q+1)q(q1)q212q212q212q212011111110q110000ii=1.
.
.
q32(q+1)λiξin+ξin01(1)i1(1)iψii=1.
.
.
q12(q1)λi0ζinζin1(1)i1(1)iεε=±1q+12λq12(1)n012+ε2r12η+ε2r12ε2r12ηε2rψεε=±1q12λq+120(1)m12+ε2r12η+ε2r12ε2r12ηε2r&)1'1`η=(1)q12xr=√ηqWGL2(q)%('3'2a+12a2a2a2a1+22a12a2a12a1+22aWWW2a1WWW1.
xD%q≡3(mod4)x2Rl7!
7@'%&$c(3232Vc$c)1!
gA)Xd%E'%&)1FCcd'11.
.
.
11111111111WWW11WWW11WWW11WWW1.
.
.
1WWW1.
icds92R&)d$cd1WWW11WWW1df)1F'32y'f7@%ERER&v12*(v1)xj%ER&d7@27@f7@%&dd"FD'2b1~)1%&de$fP71$"02FWir92R&)d$1WWW1pF7@R`cd'w32'f7@%ERER&u12*u12WXi}7s!
7@'%&$c3247@'f7@Fcd'`42222b1+22b122b12b1+21WWW12bWWW2b.
GL2(q)iT7e'f7@92R&SsW%)e32)1F2FQsR&cdr$7@f71$"'q"cd%EVc3i0Q$"'%E92R&cd432GL2(q)WiueRER&cd''%EVc32aktsG)ix@7@u%84cW§HFQr71$c$c)1Rl71327@0iha32cdd0Qde36502FQr$c)1R&)1F2FQ%EFQ3i%&D0QR&UFQ)1!
(9232e$"Rl71ddfcd4"2Vcd"FD'Vccds7@$c"''y$c)1R&)1F2FQXxA02FQy71$c$c)1Rl713232"BX7@F's02FQeRE%EuXFQ(%EFih3i%&0QeR&(FQ)1!
e92g32e$7@f71$"'q"cd"2Vcd"F'Vcds7@s$c"''yRE%EuXFQXW6Ucd%EF~)1!
7@'%&)1FQdd"B"F'H$c)1FD'"4R&cd32V~7@02'd4365%EFQ3i%7@uXW)3232¤`SsW%)7@f71$"'q"cd%EVc3i0Q$"'%E92R&cd32GL2(q)(q1)(q1)(q2)2q(q1)2(q1)αn00αnn=0.
.
.
q2αn00αmn,m=0.
.
.
q2n.
.
q22q+1nαn10αnn=0.
.
.
q2q(q+1)q(q1)q21(q1)ii=0.
.
.
q2ξ2inξi(n+m)ξinξ2in(q1)ii=0.
.
.
q2qξ2inξi(n+m)ξin0(q1)(q2)2iji,j=0.
.
.
q2i.
.
q22q+1i(q1)ξin0ζinζqinξin&)1'1`γβn00βqnγβqn00βnxψi=ψqi)'aqicd'$c)1!
g2'V!
#)d3i02R&)q21WHFbj)Xdγ=βqβ11∈GL2(q2)WGL2(q))32%icd$7@f71$"'q"cd3i092R&)D$2%EFQ$"%E7@RTd)1F'0`λuA)102λ=0.
.
.
2a1xλuA)102λ=0.
.
.
2a1xλuuA)102λ,=0.
.
.
2a1λ.
.
2a+b12bλWi92R&)d$r2%EFQ$"%E7@Rj32GL2(q)$c)1FD'%&"F'32"0is$7@f71$"'q"cdf!
#)d3i02Rl7@%Ecd%EVc3i0Q$th'%E92R&cdxR&s$7@f71$"'q"s'%EBd%l7@R6"'02F$7@f71$"'q"3232"uXVq1xiV"u7@ReRl7cd1F36502FC$7@f71$"'q"ψλuv7@0is2haV"R&V"!
#"F'dWxi7y!
7@'%&$c(3232Vc$c)1!
gj)Xd%E'%&)1FIcd'rRl7gd02%EBX7@F'1`1···11···12···20···00···01···11···11···12a2a2a1(2a1)2a1(2b1)"'df7y!
7@'%&$c(32(7@'f7@FCcd'2a2a+12a2a2a1+2b1.
2V$4(8@"§¨C72A!
CGL2(q)icdU'f7@92R&cdSW%"'SsW%4y32)1F2FQ"FD'rR&cdU$7@f71$"'q"cd%EVc3i0Q$"'%E92R&cdr32He"'HsxFQ)1!
7@RE%&df7@'"02dH32cd4')1cdTe"'Tsx"'432R&"02dhad)10Qdh{uX)102jcd432exDdR&)(6Pe"'Psd%$c"0isDha$"%}d)1F'FQ)1Fih{'%EBd%l7@0is6Wicde'f7@92R&cdeSsW%8b"'ySsW%9b32)1F2FQ"F'R&cde$7@f71$"'q"cde%EVc3i0Q$"'%E92R&cdcdAc$"'%EBth!
#"F'32Hex`FQ)1!
7@RE%&d7@'"02e36502F)had)10Qdh{uX)102jg32xDdR&)(6d%q≡1(mod4)x"'32HsxiFQ)1!
7@RE%&d7@'"02H36502F)had)10Qdh{uX)102A32(xDdR&)(6zd%q≡3(mod4)WHFf7@2A"RER&rD0QUR{5k)1FgFQ)1'P02F)had)10Qdh{uX)102jr32xDDR&)F632SL2(q)xX"'eD0Qd%q≡±3(mod8)7@R&)1dH)1F732cd4%&d)1!
#)12P2%&d!
#cdPQ8"'NSL2(q)(P)Q8C3WQiT7'f7@92R&(SW%y32)1F2FQR&cd$7@f71$"'q"cd4%EVc3i0Q$"'%E92R&cd32Q8C3Wxd)1%E'H=NGL2(q)(P)WiTcdU$7@f71$"'q"cd%EVc3i0Q$"'%E92R&cdr32Hd)1FD'U32)1F2FQVcdU7@Rl7y'f7@92R&SsW%`gd%q≡5(mod8)xQ"'r7@4Rl7y'f7@92R&SsW%('d%q≡3(mod8)W)323)¤`SsW%7@f71$"'q"cd4%EVc3i0Q$"'%E92R&cd32He(q1)(q1)(q2)2(q1)αn00αnn=0.
.
.
q2αn00αmn,m=0.
.
.
q2n.
.
q2q1(q1)χii=0.
.
.
q2ξ2inξi(n+m)ξin(q1)χii=0.
.
.
q2ξ2inξi(n+m)ξin(q1)(q2)2χiji,j=0.
.
.
q2i.
.
q2γβn00βqnn=1.
.
.
q22q+1nγ0βnβqn0n=0.
.
.
q2q+1(q1)χii=0.
.
.
q2ξ2inξinξin(q1)χii=0.
.
.
q2ξ2inξinξinq(q1)2χii=1.
.
.
q22q+1i2ξinζin+ζqin&)1'1`γβn00βqnγβqn00βnxχi=χqi)'aqicd'$c)1!
g2'V!
#)d3i02R&)q21WGL2(q))32¤`SsW%87@f71$"'q"cd%EVc3i0Q$"'%E92R&e32He(q1)q12(2a1)(q1)αn00αnn=0.
.
.
q2αn00αnαmn=0.
.
.
q2m=1.
.
.
2a10αnαnαm0n=0.
.
.
u1m=0.
.
.
2a12a(q1)χii=0.
.
.
q2ξ2inξ2inξimξ2inξim(q1)χii=0.
.
.
q1ξ2inξ2inξimξ2inξimq12(2a1)χiji=0.
.
.
q2j=0.
.
.
2a12ai2j2ξinξin(ξjm+ξ(ji)m)&)1'`αn00αnαmαnαm00αnxχij=χiji)'aijcd'U$c)1!
g2'V!
#)d3i02R&)2aW¤¤`SsW%97@f71$"'q"cd4%EVc3i0Q$"'%E92R&cdH32Hs(q1)q12(2b1)(q1)αn00αnn=0.
.
.
q2βn00βqnn=1.
.
.
2b(q1)12bn0βnβqn0n=0.
.
.
2b12b(q1)χii=0.
.
.
q2ξ2binξinξin(q1)χii=0.
.
.
q2ξ2binξinξinq12(2b1)χii=1.
.
.
2b(q1)12bi2ξinζin+ζqin&)1'`βn00βqnβqn00βnxχi=χqi)'aqicd'r$c)1!
g2'Vs!
#)D3i02R&)2b(q1)W)324¤SsW%7@f71$"'q"cdH%EVc3i0Q$"'%E92R&cd32Q8C3h%±{hI,hJ,hK}AAA2A294444χ0χ1%%%ωωω2ω2χ2%%%ω2ω2ωωχ0)h)2h%%h%%χ1)h)2ωωω2ω2χ2)h)2ω2ω2ωωχh%2222&)1'1`ωcd'r02FQf71$"%EFQ')1%&d%&q"!
#32R{502F2%E'VXW¤`SW%`7@f71$"'q"cd4%EVc3i0Q$"'%E92R&cdH32H$q≡5(mod8))(q1)q12(q1)(q1)q12αn00αnn=0.
.
.
q2αn00αnn=0.
.
.
q32αn00ααnn=0.
.
.
q2αnAn=0.
.
.
q20αnααn0n=0.
.
.
q32(q1)χii=0.
.
.
q2ξ2in(1)iξ2inξiξ2inξ2in(ξ)iξ2in(q1)χii=0.
.
.
q22ξ(2i+1)n0(1+ξ)ξiξ(2i+1)nξ(2i+1)n0q12χ(4)ii=0.
.
.
q322ξ2in2(1)iξ2in0ξ2in0(q1)χii=0.
.
.
q23ξ2in(1)iξ2inξiξ2in0(ξ)iξ2inq12χii=0.
.
.
q324ξ(2i+1)n00ξ(2i+1)n0A4§S4)3238¤`SsW%('7@f71$"'q"cd%EVc3i0Q$"'%E92R&cd32H$q≡3(mod8)&(q1)q12(q1)q12(q1)αn1001n=0.
.
.
q2αnhIn=0.
.
.
q32αnAn=0.
.
.
q2αnBn=0.
.
.
q32αnhJBn=0.
.
.
q268126(q1)χii=0.
.
.
q2ξ2inξ2inξ2inξ(2n+1)iξ(2n+1)i(q1)χii=0.
.
.
q22ξ(2i+1)n0ξ(2i+1)n0ξ(2i+1)n+iζ2(ζ3uζu)q12χ(4)ii=0.
.
.
q322ξ2in2ξ2inξ2in00(q1)χii=0.
.
.
q23ξ2inξ2in0ξ(2n+1)iξ(2n+1)iq12χii=0.
.
.
q324ξ(2i+1)n0ξ(2i+1)n00A4C$S4xd)1%E'A4R&uX)102j#32cdj"!
(02'f7@'%&)1FQde7@%Ecd(36502Fo"FQd"!
e92R&4CV"R&V"!
#"FD'dWHF#$PQ)1%&d%E'f3Q7@FQdA402FQr32)10292R&r'f7@FQdj)Xd%E'%&)1Fτ"'e02Fha$"d$"R&σWXicdw"2Vcd"Fih'f7@'%&)1FQdf%EVc3i0Q$"'%E92R&cd32A4d)1F'R&cdd02%EB17@FD'cd$)1Fm$PQ)1%&d%E'U02FQ4f71$"%EFQ4')1%&d%&q"!
#32sR{502F2%E'Vj&`eτσσ21344χ11111χj11jj2χj211j2jχ33100.
icd$7@f71$"'q"cdH!
#)D3i02Rl7@%Ecd4%EVc3i0Q$"'%E92R&cd432A4df)1F'`eσσ21111j1jj2j21j2j.
icdr!
7@'%&$ccdH3232Vc$c)1!
gA)Xd%E'%&)1FI"'32e7@'f7@FCdf)1F'`)3239100101010011211121112.
xd)1%E'S4R&uX)102j32cdj"!
(02'f7@'%&)1FQds36502FC"FQd"!
e92R&e4V"R&V"!
#"F'dWjHFC32Vthd%EuXFQ7@τ02FQ'f7@FQdj)Xd%E'%&)1Fxτ02FQb32)10292R&'f7@FQdj)Xd%E'%&)1Fxσ02F$"i$"R&32R&)1F2uX0Q"02"'ρ02Fm$"i$"R&s32HR&)1F2uX0Q"024QW))1%&$"%6Rl7('f7@92R&32cdU$7@f71$"'q"cd%EVc3i0Q$th'%E92R&cdH32S4$R&cdFQ)1!
#dH32cd4$7@f71$"'q"cdH2)Bd%&"F2FQ"F's32($c"0isb32cd4$7@f71$"'q"cd32HxF!
'f7@92R&cdSsW%`g"'SsW%('xQ"'2)12%&V"'V%W4QW08&`eτστρ13866χ011111χ2u11111χ031011χ2u31011χ(4)022100.
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