Centres of cyclotomic Hecke algebras

Speaker: Andrew Francis

Affiliation: University of Western Sydney

Time: Monday 18/10/2010 from 14:00 to 15:00

Venue: Access Grid UWS. Presented from Parramatta (EB.1.32), accessible from Campbelltown (26.1.50) and Penrith (Y239).

Abstract: This is joint work with John Graham and Lenny Jones.

In this talk I will run through our recent proof of the claim that the centres of cyclotomic Hecke algebras are precisely the set of symmetric polynomials in analogues of the Jucys-Murphy elements.

Cyclotomic Hecke algebras are important algebras in numerous applications, for instance in knot theory, in representation theory, and even statistical mechanics. They are a generalization of the well-studied Iwahori-Hecke algebras, which are closely related to the symmetric groups -- perhaps the most familiar of all non-commutative algebraic structures.

The centre of an algebra -- the set of elements that commute with all other elements of the algebra -- is an important feature of its structure, giving information about its irreducible representations. The link between symmetric polynomials in certain elements and the centre has been noted in a wide family of related algebras. This result establishes this fact in one of the important remaining families of algebras.

The talk will involve relationships between several algebras, particularly the affine Hecke algebras, but a lot of it will focus on the link with affine braid groups. There will be pictures!

Biography: Andrew Francis is a Professor and ARC Future Fellow in the Centre for Research in Mathematics in the School of Computing and Mathematics at UWS. His research interests lie in algebra (finite reflection groups and Hecke algebras), in mathematical biology (evolutionary questions related to bacterial genetics), and in applications of algebra to biology.