An analogue of ladder representations for classical groups

TL;DR

This paper introduces ladder representations for classical groups over non-archimedean fields, expanding the understanding of their structure and duals, with explicit computations and formulas for these representations.

Contribution

It defines ladder representations for split odd special orthogonal and symplectic groups, including their Jacquet modules, Aubert duals, and a formula relating them to standard modules.

Findings

Ladder representations form a natural class in the admissible dual.

Explicit formulas for Jacquet modules and Aubert duals are provided.

Ladder representations can be expressed as linear combinations of standard modules.

Abstract

In this paper, we introduce a notion of ladder representations for split odd special orthogonal groups and symplectic groups over a non-archimedean local field of characteristic zero. This is a natural class in the admissible dual which contains both strongly positive discrete series representations and irreducible representations with irreducible A-parameters. We compute Jacquet modules and the Aubert duals of ladder representations, and we establish a formula to describing ladder representations in terms of linear combinations of standard modules.