On representations induced from the Zelevinsky segment and a tempered representation in the half-integral case

Abstract

Let [Formula: see text] denote either the group [Formula: see text] or [Formula: see text] over a non-archimedean local field of characteristic zero. We determine the reducibility criteria for a parabolically induced representation of the form [Formula: see text], where [Formula: see text] denotes the Zelevinsky segment representation of the general linear group attached to the segment [Formula: see text], with [Formula: see text] half-integral, and [Formula: see text] denotes an irreducible tempered representation of [Formula: see text].