Représentations de réduction unipotente pour SO(2n + 1), III : Exemples de fronts d’onde

Waldspurger, Jean-Loup

doi:10.2140/ant.2018.12.1107

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Représentations de réduction unipotente pour $\mathrm{SO}(2n+1)$, III: Exemples de fronts d'onde

Jean-Loup Waldspurger

Vol. 12 (2018), No. 5, 1107–1171

DOI: 10.2140/ant.2018.12.1107

Abstract

Soit $G$ un groupe $SO (2 n + 1)$ défini sur un corps $p$ -adique. Nous calculons le front d’onde des représentations irréductibles anti-tempérées de $G (F)$ qui sont de réduction unipotente. Le front d’onde d’une telle représentation est l’orbite orthogonale duale à l’orbite symplectique qui intervient dans le paramètre d’Arthur de cette représentation.

Let $G$ be a group $SO (2 n + 1)$ defined over a $p$ -adic field. We compute the wave front set of the antitempered irreducible representations of $G (F)$ which are of unipotent reduction. The wave front set of such representations is the orthogonal orbit dual to the symplectic orbit appearing in the Arthur’s parametrization of the representation.

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Keywords

representation of unipotent reduction, dual orbit, wave front set, unipotent orbit

Mathematical Subject Classification 2010

Primary: 22E50

Milestones

Received: 17 February 2017

Revised: 22 January 2018

Accepted: 23 February 2018

Published: 31 July 2018

Authors

Jean-Loup Waldspurger
CNRS IMJ-PRG Paris France

Vol. 12, No. 5, 2018