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"1F$7#<#""#7#7$Q"eF$7#<#"""F$
