Vol. 2, No. 1, 2020

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Fronts d'onde des représentations tempérées et de réduction unipotente pour $\mathrm{SO}(2n+1)$

Jean-Loup Waldspurger

Vol. 2 (2020), No. 1, 43–95
Abstract

Soit G le groupe spécial orthogonal SO(2n + 1) défini sur un corps p-adique F. Soit π une représentation admissible et irreductible de G(F) qui est tempérée et de réduction unipotente. On démontre que π admet un front d’onde et l’on en donne une méthode de calcul dans certains cas particuliers.

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

Keywords
representation of unipotent reduction, unipotent orbit, dual orbit, wave front set
Mathematical Subject Classification 2010
Primary: 22E50
Milestones
Received: 22 June 2018
Accepted: 20 November 2018
Published: 22 March 2019
Authors
Jean-Loup Waldspurger
CNRS IMJ-PRG
Paris
France