Abstract:

Let G=GLn(Fq) be the general linear group over a finite field. The Jacquet module is an important tool for understanding the structure of representations of G. For a cuspidal representation of G, the Jacquet module is always trivial, which motivates the study of its twisted versions. In this talk, we will discuss recent results about the structure of twisted Jacquet modules for cuspidal representations of G. This is based on joint work with Kumar Balasubramanian and Krishna Kaipa.