Algebra Seminar

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, u₁, ...,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).