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$Q-121321421324F$7#<#"#;7&7$Q,12132142132F$7#<#"#77$Q,12132421324F
$7#<#"#87$Q,12321421324F$7#<#"#97$Q,21321421324F$7#<#"#:7%7$Q+2132142132F$7#<#"
"*7$Q'121421F$Fap7$Q)13214213F$Ffp7%7$Q+2132421324F$7#<#"#57$Q'121321F$F\p7$Q)1
3421324F$Ffp7%7$Q+1213242132F$7#<#""'7$Q)12324213F$Ffp7$Q'232423F$F[q7*7$Q&2134
2F$7#<#""$7$Q$121F$Fer7$Q&12321F$7#<#""(7$Q&12421F$7#<#"")7$Q$232F$Faq7$Q$242F$
F[r7$Q&32423F$7#<#"#67$Q$134F$Ffp7%7$Q%2142F$F_s7$Q'321423F$7#<#""%7$Q#14F$F[t7
%7$Q%2132F$F_s7$Q'421324F$7#<#""&7$Q#13F$Ffs7%7$Q'123421F$7#<#""#7$Q%2342F$F_s7
$Q#34F$Fdt7&7$Q"1F$F`v7$Q"2F$F_s7$Q"3F$F^u7$Q"4F$Fhu7#7$Q"eF$7#<#"""F$
