The number of simple modules of the Hecke algebras of type G(r,1,n)

Susumu Ariki and Andrew Mathas


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


Math. Zeitschrift, 233 (2000), 601-623.


This paper is concerned with the problem of classifying the simple modules of a Hecke algebra 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 the affine Hecke algebras of type A.

The paper are available in the following forms:

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Alternatively, you can request a copy by e-mailing me.

Andrew Mathas
8th July 1998