Fronts d'onde des repr{\'e}sentations temp{\'e}r{\'e}es et de r{\'e}duction unipotente pour SO(2n + 1)

TL;DR

This paper proves that tempered, unipotent-reduction representations of SO(2n+1) over p-adic fields have wave front sets and provides a method to compute them in specific cases like discrete series.

Contribution

It establishes the existence of wave front sets for a class of representations and offers a computational method for certain cases, advancing understanding of representation theory of SO(2n+1).

Findings

Tempered, unipotent-reduction representations have wave front sets.

Method to compute wave front sets for discrete series.

Results enhance understanding of representation structure for SO(2n+1).

Abstract

Let G be a special orthogonal group SO(2n+1) defined over a p-adic field F. Let $\pi$ be an admissible irreducible representation of G(F) which is tempered and of unipotent reduction. We prove that $\pi$ has a wave front set. In some particular cases, for instance if $\pi$ is of the discrete series, we give a method to compute this wave front set.