# Tau Infinity Invariants for g = A1
#
# This file enumerates the primitive ideals of the universal enveloping algebra of A1
# at infinitesimal character rho and their tau infinity invariants.
#
# The enumeration of primitive ideals is provided via the Barbasch-Vogan-Joseph
# classification scheme; wherein the primitive ideals at infinitesimal character rho
# correspond to pairs [O,i], where 0 is a special nilpotent orbit of g and i is an
# index running from 1 to the dimension of the irreducible special representation of
# W attached to O via the Springer correspondence.
#
# Tau infinity invariants are finite sequences of sets of tau invariants. Below we represent
# tau invariants as integers between 1 and 2^(rank(g)); corresponding to their order in a
# shortlex listing of the power set 2^{rank(g)}.
#
# For each primitive ideal, we also provide the corresponding Duflo involution in W.
# At infinitesimal character rho, the primitive ideals in U(g) are in a 1:1
# correspondence with the left cells of W. Each left cell of W contains a unique Duflo
# involution. The primitive ideal corresponding to a Duflo involution w is, in fact,
# realized as the annihilator of the simple highest weight module with highest weight
# lambda = -w.rho - rho.
#
## special orbit #1: , [1, 1]
## special rep [1, 1] , dim = 1
tii[1,1] := [{2}]:
di[1,1] := "1":
## special orbit #2: , [2]
## special rep [2] , dim = 1
tii[2,1] := [{1}]:
di[2,1] := "":