The number of simple modules of the Hecke algebras of type G(r,1,n)
Susumu Ariki and Andrew Mathas
Research Report 98-14
Date: 8 July 1998
This paper is concerned with the problem of classifying the simple modules
of a Hecke algebra H of type G(r,1,n). Using Kac-Moody algebra
techniques we first show that the number of simple H-modules is, in
a certain sense, independent of the choice of parameters for the Hecke algebra.
Next, by studying Kashiwara's crystal graph, we show that the simple
H-modules are indexed by the set of Kleshchev
multipartitions and we give a generating function for this set.
As an application of these results we give a classification of the number
of simple modules of an affine Hecke algebra of type A.
Cyclotomic Hecke algebras. Affine Hecke algebras. Kac-Moody algebras.
Crystal graphs. Quantum groups.
AMS Subject Classification (1991)
Primary: 17B67, 20G05
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