Shalika models of GL(4) over a finite field

Abstract

The goal of this paper is to determine whether a irreducible representation of GL(4) over a finite field admits a shalika model We analysis it for two parts:cuspidal representations and noncuspidal representations For cuspidal representations we use a result published from mathematician Dipendra Prasad at 2000 From the result it is easy to determine whether a cuspidal representation has a Shalika model For noncuspidal representations by the definition of cuspidal we see a noncuspidal representation as a subrepresentation of an parabolic induction from some parabolic induction subgroup of GL(4) We consider all parabolic inductions of GL(4) and use a well-known theorem Mackey’s theorem to determined whether a parabolic induction has a Shalika model From Mackey’s theorem we get some condition for a parabolic induction has a Shalika model and use it to get some result

Date of Award	2018 Jul 10
Original language	English
Supervisor	Chufeng Nien (Supervisor)