Square integrability of representations on p-adic symmetric spaces

TL;DR

This paper extends Casselman's criterion to p-adic symmetric spaces, providing a new characterization of when representations are square integrable based on exponents of Jacquet modules.

Contribution

It introduces a symmetric space analogue of Casselman's criterion, linking square integrability to exponents of Jacquet modules in the p-adic setting.

Findings

Established a symmetric space version of Casselman's criterion.

Characterized square integrability via exponents of Jacquet modules.

Provides a new tool for analyzing representations on p-adic symmetric spaces.

Abstract

A symmetric space analogue of Casselman's criterion for square integrability of representations of a p-adic group is established. It is described in terms of exponents of Jacquet modules along parabolic subgroups associated to the symmetric space.