Dimension formula for the twisted Jacquet module of a cuspidal representation of $\GL(2n,\mathbb{F}_q)$

Abstract

Let $F$ be a finite field and $G=\GL(2n,F)$. In this paper, we calculate the dimension of the twisted Jacquet module $\ddot{I}{€}_{N,\ddot{I}{ˆ}_A}$ where $A\in \M(n,F)$ is a rank $k$ matrix and $\ddot{I}€$ is an irreducible cuspidal representation of $G$.

This is a preliminary draft. arXiv admin note: text overlap with arXiv:2206.03024, arXiv:2206.02634