## University of Sydney Algebra Seminar

# John Graham

## Friday 15th October, 12.05-12.55pm, Carslaw 175

### On the centre of the Ariki-Koike Algebra

The Ariki-Koike algebra H(R,q) is a quotient of the (extended) affine Hecke algebra associated to the general linear group. The centre of the affine Hecke algebra has a well known description in terms of the Weyl group action on the weight lattice due to Bernstein. In the talk, I discuss a proof that (over an arbitrary unital commutative ring R) the centre of the Ariki-Koike algebra is the image of the centre of the affine Hecke algebra if q-1 is invertible in R. One of the key ingredients is a description of the trace functions on the affine Hecke algebra and its relationship to trace functions on the Ariki-Koike Hecke algebra. This is joint work with Andrew Francis and Lenny Jones.