Subrepresentation Theorem for p-adic Symmetric Spaces

TL;DR

This paper introduces the concept of relative cuspidality for representations on p-adic symmetric spaces, characterizes it via Jacquet modules, and generalizes Jacquet's subrepresentation theorem to this setting.

Contribution

It presents the first characterization of relative cuspidality and extends Jacquet's subrepresentation theorem to p-adic symmetric spaces.

Findings

Characterization of relative cuspidality using Jacquet modules

Generalization of Jacquet's subrepresentation theorem

Framework for analyzing distinguished representations on p-adic symmetric spaces

Abstract

The notion of relative cuspidality for distinguished representations attached to $p$-adic symmetric spaces is introduced. A characterization of relative cuspidality in terms of Jacquet modules is given and a generalization of Jacquet's subrepresentation theorem to the relative case (symmetric space case) is established.