On Jacquet modules of representations of segment type

Abstract

Let G n denote either the group Sp(n, F) or SO(2n + 1, F) over a local non-archimedean field F. We study representations of segment type of group G n , which play a fundamental role in the constructions of discrete series, and obtain a complete description of the Jacquet modules of these representations. Also, we provide an alternative way for determination of Jacquet modules of strongly positive discrete series and a description of top Jacquet modules of general discrete series.