On Jacquet modules of representations of segment type

TL;DR

This paper provides a comprehensive analysis of Jacquet modules for segment-type representations of Sp(n) and SO(2n+1, F), crucial for understanding discrete series in non-archimedean local fields.

Contribution

It offers a complete description of Jacquet modules for these representations and introduces an alternative method for strongly positive discrete series.

Findings

Complete description of Jacquet modules for segment-type representations

New method for determining Jacquet modules of strongly positive discrete series

Description of top Jacquet modules of general discrete series

Abstract

We study representations of segment type of groups Sp(n) and SO(2n+1, F) over a local non-archimedean field, 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. In this version are corrected few typographical errors which exist in the published version of this paper (see page 5 of the paper for more details).