Weil representations of finite general linear groups and finite special linear groups

Pham Huu Tiep

Vol. 279 (2015), No. 1-2, 481–498

DOI: 10.2140/pjm.2015.279.481

Abstract

Let $q$ be a prime power and let $G_n$ be the general linear group ${GL}_n\left(q\right)$ or the special linear group ${SL}_n\left(q\right)$, with $n\ge 4$. We prove two characterization theorems for the Weil representations of $G_n$ in any characteristic coprime to $q$, one in terms of the restriction to a standard subgroup $G_{n-1}$, and another in terms of the restriction to a maximal parabolic subgroup of $G_n$.

Dedicated to the memory of Professor R. Steinberg

Keywords

Weil representations, finite general linear groups, finite special linear groups

Mathematical Subject Classification 2010

Primary: 20C15, 20C20, 20C33

Milestones

Received: 9 March 2015

Revised: 22 July 2015

Accepted: 23 July 2015

Published: 21 December 2015