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$Q0121321432154321F$7#<#"#K7'7$Q+1213214321F$7#<#"#F7$Q-1213214543
21F$7#<#"#G7$Q/12132432154321F$7#<#"#H7$Q-123243254321F$7#<#"#I7$Q+2324325432F$
7#<#"#J7+7$Q*121432154F$7#<#"#=7$Q,13214321543F$7#<#"#?7$Q.1232143254321F$7#<#"
#@7$Q.2132143215432F$7#<#"#B7$Q,23214325432F$7#<#"#C7$Q*213435432F$7#<#"#D7$Q(1
213215F$Fap7$Q,12134354321F$Ffp7$Q(1343543F$F[q7'7$Q-213243215432F$7#<#"#77$Q+1
324321543F$F[r7$Q)13214543F$F`r7$Q+2132145432F$Fjr7$Q'121454F$Ffp7,7$Q'121321F$
7#<#"#<7$Q)12134321F$Ffq7$Q+1213454321F$7#<#"#>7$Q)12324321F$F[r7$Q+1232454321F
$F`r7$Q+1234354321F$7#<#"#A7$Q'232432F$Fer7$Q)23245432F$Fjr7$Q)23435432F$F_s7$Q
'343543F$7#<#"#E727$Q'132143F$7$<#"")<$"#6Fhq7$Q)12432154F$7$<#""*<$F]tFbr7$Q)2
1321432F$7$<#F^w<$F\wF]t7$Q'243254F$7$F\t<%Fcw"#9F\s7$Q'213432F$7$F\t<%F^w"#8F]
r7$Q)21345432F$7$<#FcxFdw7$Q)32432543F$7$<#F^x<$F]t"#:7$Q'324543F$7$<#F]y<$F^xF
as7$Q%1214F$7$Fgq<&F\wFcwF]tFbu7$Q%1215F$7$Fau<%FcxFhqFbr7$Q%1343F$7$F\r<'F\wFc
wF]tF^xFbr7$Q'123215F$7$Far<&F\wFcwFbuF\s7$Q'134543F$7$Far<&FcxF]yF]rF[v7$Q%145
4F$7$Fju<%FcwFbrFas7$Q%2325F$7$F[s<'F^wF]tFcxF]yFbr7$Q%2454F$7$F`s<&F]tFcxF]yF[
v7'7$Q*321432543F$7#<#""%7$Q&14354F$7#Fbw7$Q(2143254F$F[t7$Q&21325F$7#Fgx7$Q$13
5F$F`r7,7$Q$121F$7#<#""(7$Q&12321F$7#F[w7$Q(1234321F$F[\l7$Q*123454321F$7#<#"#5
7$Q$232F$7#Fhw7$Q&23432F$F[t7$Q(2345432F$F`\l7$Q$343F$7#F[y7$Q&34543F$7#Fay7$Q$
454F$7#<#"#;7+7$Q%2132F$7#<#""$7$Q%3243F$Ff[l7$Q%4354F$7#<#""&7$Q#13F$F[]l7$Q#1
4F$F[\l7$Q#15F$F`]l7$Q#24F$F[t7$Q#25F$F`\l7$Q#35F$F_^l7'7$Q"1F$7#<#""#7$Q"2F$Fh
^l7$Q"3F$Ff[l7$Q"4F$F__l7$Q"5F$7#<#""'7#7$Q"eF$7#<#"""F$
