University of Sydney Algebra Seminar

James Parkinson (University of Sydney)

Friday 9th September, 12.05-12.55pm, Carslaw 275

Buildings and Hecke algebras

In this talk we will discuss how the combinatorics of affine buildings can be used to give a geometric and combinatorial description of the centres of affine Hecke algebras and of Macdonald polynomials. In particular, certain structure constants in the Hecke algebra, which are not obviously nonnegative from their definition, will be seen to be nonnegative by a combinatorial argument.

If time permits we will discuss how our results can be used to obtain a generalisation of known results on spherical functions on groups of p-adic type.