Jacquet modules and irrreducibility of induced representations for classical p-adic groups

Abstract

Let G be a classical p-adic group. If T is an irreducible tempered representation of such a group and $$\rho $$ an irreducible unitary supercuspidal representation of a general linear group, we can form the parabolically induced representation $$\text{ Ind }_P^G (|det|^y \rho \otimes T)$$ . The main result in this paper is the determination for which $$y \in {\mathbb R}$$ the induced representation is reducible. The key technical result in establishing this is the determination of a certain Jacquet module subquotient.