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$Q9121321323432132343213234F$7#<#"#;7&7$Q41213213234321324321F$7#<
#"#77$Q6121321432132343213234F$7#<#"#87$Q6123213432132343213234F$7#<#"#97$Q4232
3432132343213234F$7#<#"#:7+7$Q71232132343213234321323F$7$<#""(<$""*Fcp7$Q721321
32343213234321323F$7$<#Feq<$Fcq"#57$Q72132132432132343213234F$7$<#F[r<$FeqFhp7$
Q11213213234321323F$7$F]p<$FcqFcp7$Q3121432132343213234F$7$Fbp<$F^pFhp7$Q512132
134321323432132F$7$Fbp<%FcqF[rFhp7$Q3123213432132343213F$7$Fgp<$FcpF]q7$Q513213
432132343213234F$7$Fgp<%FcqF[rFcp7$Q12321343213234323F$7$F\q<$F[rFhp7*7$Q013213
2343213243F$Faq7$Q221321323432132432F$Fhq7$Q42132432132343213234F$7$F_r<%Feq"#6
Fhp7$Q6321323432132343213234F$7$<#FbtF_r7$Q.1213234321324F$F[s7$Q21343213234321
3234F$7$FgpFjq7$Q,12323432134F$7$Fgp<%FbtFcpF]q7$Q*232343234F$7$F\qFgp7*7$Q6121
321324321323432132F$7$<#""'Fbq7$Q41232132432132343213F$7$Fbq<%FhuFeqFcp7$Q22321
3243213234323F$Fhq7$Q0213214321323432F$F^r7$Q*121321323F$7$F]pFbp7$Q21213214321
3234321F$7$FbpFjq7$Q,12143213234F$7$Fbp<%FhuF^pFhp7$Q.1321432132343F$Fcs7.7$Q)2
1321432F$7$<#""$Fbq7$Q)32134323F$7$<#""%F_r7$Q)12132132F$7$Fgu<$FbwFcq7$Q'13214
3F$7$Fbq<%FbwFgwFcp7$Q'123213F$7$Fbq<%Fhu"")Feq7$Q)12432134F$7$<#FdxFjq7$Q%2323
F$7$Fiq<&FbwFgwFcqF[r7$Q'213432F$7$F_r<%FbwFgwFhp7$Q'243234F$7$F_r<%FdxFeqFbt7$
Q)32343234F$7$Fft<$FgwF[r7$Q%1214F$7$Fbp<&FhuFcqFdxF[r7$Q%1343F$7$Fgp<&FcqFdxF[
rFbt7*7$Q,21323432132F$7$Faw<$FgwFcq7$Q(3234323F$Few7$Q.3213234321323F$7$Ffw<$F
bw""&7$Q0432132343213234F$7$<#F\[lFfw7$Q*132343213F$7$Fbq<%FbwFgwFdx7$Q(1234321
F$Fgx7$Q&23432F$7$F_r<&FbwFgwFdxFbt7$Q$343F$Fgy7*7$Q0123214321324321F$7$<#""#Fa
w7$Q(2132132F$F`w7$Q.2321432132432F$7$Faw<$Fb\lFgw7$Q,32143213243F$7$Ffw<$FbwF[
r7$Q$121F$Fjw7$Q&13213F$7$Fbq<&FbwFgwFhuFdx7$Q(1432134F$Fgx7$Q*214321324F$7$F_r
Fd[l7+7$Q)12324321F$F`\l7$Q'232432F$Fg\l7$Q%2132F$Fdz7$Q'321323F$Fjz7$Q%3243F$F
[]l7$Q)43213234F$F_[l7$Q#13F$7$Fbq<&Fb\lFbwFgwFdx7$Q#14F$Fgx7$Q#24F$7$F_r<&FbwF
gwF\[lFdx7&7$Q"1F$7#Fa\l7$Q"2F$7#Faw7$Q"3F$7#Ffw7$Q"4F$7#F`[l7#7$Q"eF$7#<#"""F$
