Special functions over finite Chevalley groups
演讲者
曲烜彤
时间
2024年04月23日 16:00 至 17:00
地点
A6-101
线上
Zoom 873 9209 0711
(BIMSA)
摘要
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.