M7R0
I+PIDataInfot+6"F$F$F$C7-%'printfG6#Q`oThe~file~GT_PIData.m~provides~two~critic
al~datums~that~independently|+F$-F'6#Qcoparameterize~the~primitive~ideals~of~Gt
~at~infinitesimal~character~rho.|+F$-F'6#QjoTo~each~primitive~ideal~I~in~U(g),~
there~corresponds~a~unique~Duflo~involution|+F$-F'6#Qeow~in~W~such~that~I~=~ann
ihilator~of~the~simple~highest~weight~module~with|+F$-F'6#QCwith~highest~weight
~-w.rho~+~rho.|+F$-F'6#QhoA~primitive~ideal~I~can~also~be~characterized~by~its~
tau_infinity~invariant.|+F$-F'6#Q$If|+F$-F'6#Q;~~~~~PRDT~:=~PIData[soi]:|+F$-F'
6#Qgothen~PRDT~is~a~list~of~datum~pairs~for~the~primitive~ideals~attached~to~th
e|+F$-F'6#QTsoi^th~special~nilpotent~orbit~of~Gt.~If,~further,|+F$-F'6#Q7~~~~~p
rdt~:=~PRDT[k]:|+F$-F'6#Qcpthen~prdt~holds~data~for~the~k^th~primitive~ideal~at
tached~the~soi^th~special~nilpotent|+F$-F'6#Qaporbit~(here~k~runs~from~1~to~the
~dimension~of~the~corresponding~special~rep~of~W)~and|+F$-F'6#Qfp~~~~~prdt[1]~=
~the~shortlex~reduced~word~expression~for~the~corresponding~Duflo~involution|+F
$-F'6#QP~~~~~prdt[2]~=~the~tau_infinity~invariant~of~I|+F$-F'6#QipSo,~in~fact,~
prdt[1]~and~prdt[2]~actually~independently~prescribe~the~primitive~ideal~indexe
d|+F$-F'6#Q/by~soi~and~k.|+F$-F'6#Qbp(Note:~tau_infinity~invariants~are~certain
~sequences~of~collections~of~tau-invariants.|+F$-F'6#QjpIn~prdt[2],~we~represen
t~tau~invariants~not~directly~as~subsets~of~the~simple~roots~of~Gt,~but|+F$-F'6
#Qbprather~by~their~index~relative~to~a~shortlex~ordering~of~the~power~set~2^(r
ank(Gt)).)|+|+F$-%'RETURNGF$F$F$F$6#""!F$,
I'PIData7,7#7$Q11213214321432434F$7#<#"#;7&7$Q.1213214321432F$7#<#"#77$Q.121324
3214324F$7#<#"#87$Q,12324321434F$7#<#"#97$Q*232432434F$7#<#"#:7(7$Q+1321432143F
$7#<#""(7$Q-213214321432F$7#<#""*7$Q/21324321432434F$7#<#"#57$Q'121321F$F\p7$Q)
12143214F$Fap7$Q-134321432434F$Ffp7*7$Q,12321432143F$7$Fbq<%"")FhqFcp7$Q.123432
1432434F$7$<#Fir<$FcqF]r7$Q*232143243F$7$FgqF^s7$Q(2134324F$7$F\r<$FhqFhp7$Q,24
321432434F$7$F\r<%FirFhq"#67$Q.3214321432434F$7$<#FjsF\r7$Q*121343214F$7$FbpF^s
7$Q&13434F$7$FgpF^s7(7$Q-321432143243F$7#<#""%7$Q'132143F$Faq7$Q)14321434F$7#F]
s7$Q)21321432F$Ffq7$Q+2143214324F$F[r7$Q%1214F$Fap7(7$Q-121324321432F$7#<#""'7$
Q+1232432143F$Faq7$Q)12343214F$F_u7$Q)23243243F$Ffq7$Q'234324F$F[r7$Q%3434F$7#F
^t7*7$Q,21324321432F$7$<#""$Fbq7$Q(3243243F$7$FitF\r7$Q$121F$7$FjuFbq7$Q*132432
143F$7$Fbq<%F\wFjtFir7$Q&12321F$7$Fbq<%F[vFirFhq7$Q(1243214F$F\s7$Q$232F$Fas7$Q
&24324F$7$F\r<&F\wFjtFirFhq7(7$Q%2132F$7#F[w7$Q%3243F$Fht7$Q'432434F$7#<#""&7$Q
#13F$Faq7$Q#14F$F_u7$Q#24F$F[r7&7$Q"1F$7#<#""#7$Q"2F$Ffx7$Q"3F$Fht7$Q"4F$F[y7#7
$Q"eF$7#<#"""F$
