### School of Mathematics and Statistics

### Andrew Mathas

University of Sydney

### Morita equivalences of Ariki-Koike algebra.

**Friday 22nd October, 12-1pm, Carslaw 375. **
An Ariki-Koike algebra *H* is an algebra attached to the
complex reflection group *W* of type *G(r,1,n)*; that
is, *W* is the wreath product of a cyclic group of order
*r* and a symmetric group of degree *n*. The algebra
*H* depends upon *r+1* parameters *q,
u*_{1}, ...,u_{r}.

The aim of this talk is to show that up to Morita equivalence
*H* can be replaced by a direct sum of tensor products of
"smaller" Ariki-Koike algebras, each with a parameter set
which consists of a single *q*-orbit; special cases of this
result were obtained previously by Dipper-James, Du-Rui and Ariki. This
result is not only interesting but was the key reduction in the
classification of the simple modules of the Ariki-Koike algebras.
Other applications will also be discussed.

This is joint work with Richard Dipper (Stuttgart).