University of Sydney Algebra Seminar

James Parkinson (University of Sydney)

Friday 19th June, 12.05-12.55pm, Carslaw 375

Random walks on affine buildings and representations of affine Hecke algebras

In this talk we discuss an approach for analysing random walks on p-adic Lie groups (groups like the group SL_3(Q_p) of 3x3 matrices with entries in the p-adics and with determinant 1). The types of walks that we are interested in are those that are well adapted to the structure of the affine building associated to the group: Namely those walks which induce radially invariant random walks on the chambers of the building.

The aim of the talk is to give an overview of the types of techniques used. The main idea is to use the representation theory of the associated affine Hecke algebra, and some harmonic analysis from the work of E. Opdam. This is very much a work in progress, in collaboration with Bruno Schapira from Paris Sud.