University of Sydney Algebra Seminar

Valentin Buciumas (University of Queensland)

Friday 14 June, 12-1pm, Place: Carslaw 375

Whittaker functions on p-adic groups and solvable lattice models

A method to study symmetric functions is to represent them as partition functions of solvable lattice models, where powerful tools like the Yang-Baxter equation can be used. In this talk I will explain how to relate (spherical/Iwahori) Whittaker functions on (covers of) p-adic groups to solvable lattice models. The proof of such a relation involves certain functional equations which can be deduced from classical results of Casselman and Shalika on the p-adic side and via the Yang-Baxter equation on the lattice model side. Time permitting, I will mention connections between the theory of p-adic and quantum groups that follow naturally from this relation. This is joint work with Brubaker, Bump and Gustafsson.