Paquets d’Arthur des groupes classiques et unitaires

Nicolás Arancibia; Colette Mœglin; David Renard

doi:10.5802/afst.1590

Nicolás Arancibia ¹; Colette Mœglin ²; David Renard ³

¹ Institut Mathématique de Jussieu
² CNRS, Institut Mathématique de Jussieu
³ Centre de Mathématiques Laurent Schwartz, École Polytechnique

Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 27 (2018) no. 5, pp. 1023-1105.

Abstract
Abstract

Let $G = G (ℝ)$ be the group of real points of a quasi-split connected reductive algebraic group defined over $ℝ$ . Assume furthermore that $G$ is a classical group (symplectic, special orthogonal or unitary). We show that the packets of irreducible unitary cohomological representations defined by Adams and Johnson in 1987 coincide with the ones defined recently by J. Arthur in his work on the classification of the discrete automorphic spectrum of classical groups (C.-P. Mok for unitary groups). For this, we compute the endoscopic transfer of the stable distributions on $G$ supported by these packets to twisted ${GL}_{N}$ in terms of standard modules and show that it coincides with the twisted trace prescribed by Arthur.

Soit $G = G (ℝ)$ le groupe des points réels d’un groupe algébrique connexe réductif quasi-déployé défini sur $ℝ$ . Supposons de plus que $G$ soit un groupe classique (symplectique, spécial orthogonal ou unitaire). Nous montrons que les paquets de représentations irréductibles unitaires et cohomologiques définies par Adams et Johnson en 1987 coïncident avec ceux definis plus récemment par J. Arthur dans son travail sur la classification du spectre automorphe discret des groupes classiques (C.-P. Mok pour les groupes unitaires). Pour cela, nous calculons le transfert endoscopique des distributions stables sur $G$ supportées par ces paquets vers le groupe ${GL}_{N}$ tordu en termes de modules standard et nous montrons qu’il est égal à la trace tordue prescrite par Arthur.

Received: 2016-11-29
Accepted: 2017-02-06
Published online: 2019-01-21

MR Zbl

DOI: 10.5802/afst.1590

Author's affiliations:

Nicolás Arancibia ¹; Colette Mœglin ²; David Renard ³

¹ Institut Mathématique de Jussieu
² CNRS, Institut Mathématique de Jussieu
³ Centre de Mathématiques Laurent Schwartz, École Polytechnique

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     author = {Nicol\'as Arancibia and Colette M{\oe}glin and David Renard},
     title = {Paquets {d{\textquoteright}Arthur} des groupes classiques et unitaires},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {1023--1105},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {6e s{\'e}rie, 27},
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     year = {2018},
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Nicolás Arancibia; Colette Mœglin; David Renard. Paquets d’Arthur des groupes classiques et unitaires. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 27 (2018) no. 5, pp. 1023-1105. doi : 10.5802/afst.1590. https://afst.centre-mersenne.org/articles/10.5802/afst.1590/

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