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Pré-Publication, Document De Travail Année : 2018

Paquets d'Arthur des groupes classiques et unitaires

David Renard
  • Fonction : Auteur
  • PersonId : 1028143
Nicolás Arancibia
Colette Moeglin
  • Fonction : Auteur
  • PersonId : 828557

Résumé

Let $G=\mathbf{G}(\mathbb{R})$ be the group of real points of a quasi-split connected reductive algebraic group defined over $\mathbb{R}$. 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.

Dates et versions

hal-01707562 , version 1 (12-02-2018)

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David Renard, Nicolás Arancibia, Colette Moeglin. Paquets d'Arthur des groupes classiques et unitaires. 2018. ⟨hal-01707562⟩
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