Speaker:  Elad Zelingher (University of Michigan) 

Title:  On gamma factors and Bessel functions of finite general linear groups

Abstract:  In the representation theory of p-adic groups, one way to study irreducible representations is by attaching local factors to them. These local  factors are complex valued functions of a complex variable, and they often encode properties of the representations in question. In this talk, I will explain an analog of these local factors for irreducible generic representations of GL(n, F_q). I will talk about two families of gamma factors for the tensor product representation (based on constructions by Jacquet--Piatetski-Shapiro--Shalika and Shahidi) and about the Bessel function of a generic representation (defined by Gelfand--Graev). I will give a conceptual quantitative interpretation for the absolute value of these gamma factors. I will also explain a relation between the Bessel function and Kloosterman sums and sheaves. This talk is based on my two recent preprints, where the most recent one is a joint work with David Soudry.