M.Sc Thesis
M.Sc Student Musiya-Oknin Avital Identities between Bessel Functions attached to Representations of Matrix Groups over a Finite Field Department of Mathematics Professor Ehud Moshe Baruch

Abstract

Let K be a finite field. In this paper we find a correspondence between irreducible representations of GL(2,K) that their central character is trivial and irreducible representations of SL(2,K). In some sense we correspond a representation to its root. The correspondence is obtained via Bessel identities between relative Bessel functions attached to representations of GL(2,K) and Bessel functions attached to representations of SL(2,K). Bessel functions were studied by Piatetski-Shapiro, while the relative Bessel functions are defined and computed here.