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

## Author

**Susumu Ariki** and **Andrew Mathas**

## Status

Research Report 98-14

Date: 8 July 1998

## Abstract

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

## Content

The paper is available in the following forms:
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- 1998-14.dvi.gz (38kB) or
1998-14.dvi (93kB)

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Sydney Mathematics and Statistics