Vol. 12, No. 5, 2018

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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
Abstract

Soit G un groupe SO(2n + 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(2n + 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