On a twisted Jacquet module of GL(2n) over a finite field

TL;DR

This paper explicitly describes a specific twisted Jacquet module of an irreducible cuspidal representation of the general linear group over a finite field, contributing to the understanding of representation theory in finite groups.

Contribution

It provides an explicit description of a twisted Jacquet module for GL(2n,F), a novel result in the representation theory of finite groups.

Findings

Explicit description of the twisted Jacquet module

Enhanced understanding of cuspidal representations

New techniques for analyzing modules over finite groups

Abstract

Let F be a finite field and G=GL(2n,F). In this paper, we explicitly describe a certain twisted Jacquet module of an irreducible cuspidal representation of G.