Kloosterman sums in representation theory of $GL(n, \mathbb{F}_q)$.

Abstract: Given a "nice" irreducible representation of $GL(n, \mathbb{F}_q)$, one can define a special matrix coefficient attached to it, called the Bessel function. Often Kloosterman sums show up as special values of these Bessel functions. In this talk, I will first explain my previous results regarding special values of Bessel functions of generic representations. I will then talk about my joint work with Oded Carmon regarding special values of Bessel functions associated to Speh representations and their relation to matrix Kloosterman sums.

algebraic geometrynumber theoryrepresentation theory

Audience: researchers in the topic

Canadian Rockies Representation Theory

Series comments: Topics include, but are not limited to, geometric and categorical aspects of the Langlands Programme. Please write to Jose Cruz for zoom instructions.