Reducibility of some induced representations of p-adic unitary groups

In this paper we study reducibility of those representations of quasi-split unitary p-adic groups which are parabolically induced from supercuspidal r epresentations of general linear groups. For a supercuspidal representation associated via Howe's construction to an admissible character, we show tha t in many cases a criterion of Goldberg for reducibility of the induced rep resentation reduces to a simple condition on the admissible character.