**SMS scnews item created by James East at Wed 13 Oct 2010 1057**

Type: Seminar

Distribution: World

Expiry: 15 Oct 2010

**Calendar1: 15 Oct 2010 1205-1255**

**CalLoc1: Carslaw 175**

Auth: jamese@bari.maths.usyd.edu.au

### Algebra Seminar

# On the centre of the Ariki-Koike Algebra

### John Graham

#### Friday October 15, 12:05--12:55pm, Carslaw 175

###### Abstract

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.

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After the seminar we will take the speaker to lunch.

See the Algebra Seminar web page for information about other seminars in the series.

James East james.east@sydney.edu.au