Paquets d’Arthur des groupes classiques et unitaires

Arancibia, Nicolás; Mœglin, Colette; Renard, David

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

Soit $G=\mathbf{G}\left(ℝ\right)$ 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 ${\mathbf{GL}}_N$ tordu en termes de modules standard et nous montrons qu’il est égal à la trace tordue prescrite par Arthur.

Let $G=\mathbf{G}\left(ℝ\right)$ 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 ${\mathbf{GL}}_N$ in terms of standard modules and show that it coincides with the twisted trace prescribed by Arthur.

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