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:

- TeX dvi format:
- 1998-14.dvi.gz (12kB) or
1998-14.dvi (32kB)

- PostScript:
- 1998-14.ps.gz (36kB) or
1998-14.ps (121kB)

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

*Andrew Mathas*

8th July 1998