On tempered and square integrable representations of classical p-adic groups

TL;DR

This paper characterizes irreducible tempered and square integrable representations of classical p-adic groups, building on Moeglin's classification, and relates invariants of these representations to Jacquet modules, aiding understanding of their structure.

Contribution

It provides a natural description of tempered representations aligned with Moeglin's classification and relates invariants of square integrable representations to subquotients of Jacquet modules.

Findings

Describes irreducible tempered representations based on square integrable classification.

Expresses invariants of square integrable representations via Jacquet module subquotients.

Analyzes behavior of invariants under representation construction and deformation.

Abstract

This paper has two aims. The first is to give a description of irreducible tempered representations of classical p-adic groups which follows naturally the classification of irreducible square integrable representations modulo cuspidal data obtained by C. Moeglin and the author. The second aim of the paper is to give description of an invariant (partially defined function) of irreducible square integrable representation of a classical p-adic group (defined by C. Moeglin using embeddings) in terms of subquotients of Jacquet modules. As an application, we describe behavior of partially defined function in one construction of square integrable representations of a bigger group from such representations of a smaller group (which is related to deformation of Jordan blocks of representations).