Algebra Seminar: Buciumas -- Whittaker functions on p-adic groups and solvable lattice models

Valentin Buciumas (University of Queensland) 

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

Title: Whittaker functions on p-adic groups and solvable lattice models 

Abstract: 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.