Reducibility of some induced representations of split classical p-adic groups

In this paper we study reducibility of representations of split classical p -adic groups induced from self-contragredient supercuspidal representations of general linear groups. For a supercuspidal representation associated vi a Howe's construction to an admissible character, we show that in many case s Shahidi's criterion for reducibility of the induced representation reduce s to a simple condition on the admissible character.