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An implementation of the generalized LusztigShoji algorithm Pramod N. Achar

Summary: An implementation of the generalized Lusztig­Shoji algorithm
Pramod N. Achar
Version 0.98, July 2008
1 Introduction
Let V be a finite-dimensional complex vector space,
and let W GL(V ) be a complex reflection group.
Let q be an indeterminate. For an irreducible char-
acter Irr(W), let R() denote its fake degree,
a polynomial in q. We define R() for reducible
characters as well, by extending linearly. Let N
be the number of reflections in W, and let =
(, ), Irr(W ) be the square matrix with entries
in Z[q] given by
, (q) = qN
R( detV ).
For Irr(W), let b() be the lowest power of q
occurring in R().
A Lusztig­Shoji datum for W is an ordered col-
lection X of disjoint subsets of Irr(W) such that for
each Irr(W), and its complex conjugate ¯ be-


Source: Achar, Pramod - Department of Mathematics, Louisiana State University


Collections: Mathematics