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Paquets d'Arthur des groupes classiques et unitaires

Abstract : 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.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-01707562
Contributor : David Renard Connect in order to contact the contributor
Submitted on : Monday, February 12, 2018 - 8:27:22 PM
Last modification on : Tuesday, November 16, 2021 - 4:13:19 AM

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  • HAL Id : hal-01707562, version 1
  • ARXIV : 1507.01432

Citation

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

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