Reducibility of some induced representations of 𝑝-adic unitary groups

Abstract

In this paper we study reducibility of those representations of quasi-split unitary p p -adic groups which are parabolically induced from supercuspidal representations of general linear groups. For a supercuspidal representation associated via Howe’s construction to an admissible character, we show that in many cases a criterion of Goldberg for reducibility of the induced representation reduces to a simple condition on the admissible character.