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.

Key phrases

Cyclotomic Hecke algebras. Affine Hecke algebras. Kac-Moody algebras. Crystal graphs. Quantum groups.

AMS Subject Classification (1991)

Primary: 17B67, 20G05
Secondary: 16G99


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