Special functions over finite Chevalley groups
Organizers
Speaker
Xuantong Qu
Time
Tuesday, April 23, 2024 4:00 PM - 5:00 PM
Venue
A6-101
Online
Zoom 873 9209 0711
(BIMSA)
Abstract
Many special functions appearing in the study of integrable systems have their finite field counterparts with extensive connections with number theory and algebraic geometry. For instance, it is well known that Gauss sums are finite field analogues of Gamma-functions and Kloosterman sums are finite field analogues of Bessel functions. In this talk I will present a new approach of studying certain special functions over finite fields using representation theory of finite Chevalley groups. Namely, I will first define finite field analogues of Gamma-functions and Whittaker functions and then identify them as matrix elements of representations of (subgroups of) general linear groups over a finite field and compare them with their counterparts defined over real groups.