Arthur’s multiplicity formula for $\protect \mathbf{GSp}_4$ and restriction to $\protect \mathbf{Sp}_4$

Toby Gee; Olivier Taïbi

doi:10.5802/jep.99

Arthur’s multiplicity formula for

{GSp}_{4}

and restriction to

{Sp}_{4}

[La formule de multiplicité d’Arthur pour

{GSp}_{4}

et restriction à

{Sp}_{4}

]

Toby Gee ¹ ; Olivier Taïbi ²

¹ Department of Mathematics, Imperial College London London SW7 2AZ, UK
² CNRS et Unité de Mathématiques Pures et Appliquées, ENS de Lyon

Journal de l’École polytechnique — Mathématiques, Tome 6 (2019), pp. 469-535.

Résumé
Abstract

Nous donnons une preuve de la classification des représentations automorphes discrètes de ${GSp}_{4}$ expliquée dans [Art04], ainsi que de la compatibilité avec les correspondances de Langlands locales pour ${GSp}_{4}$ et ${Sp}_{4}$ .

We prove the classification of discrete automorphic representations of ${GSp}_{4}$ explained in [Art04], as well as a compatibility between the local Langlands correspondences for ${GSp}_{4}$ and ${Sp}_{4}$ .

Reçu le : 2018-11-03
Accepté le : 2019-06-27
Publié le : 2019-08-18

MR Zbl

DOI : 10.5802/jep.99

Classification : 11F72, 11F46, 11F55
Keywords: Automorphic forms, trace formula, endoscopy, Arthur multiplicity formula, Siegel-Hilbert modular forms
Mot clés : Formes automorphes, formule des traces, endoscopie, formule de multiplicité d’Arthur, formes modulaires de Siegel-Hilbert

Affiliations des auteurs :

Toby Gee ¹ ; Olivier Taïbi ²

¹ Department of Mathematics, Imperial College London London SW7 2AZ, UK
² CNRS et Unité de Mathématiques Pures et Appliquées, ENS de Lyon

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {Arthur{\textquoteright}s multiplicity formula for $\protect \mathbf{GSp}_4$ and restriction to $\protect \mathbf{Sp}_4$},
     journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
     pages = {469--535},
     publisher = {\'Ecole polytechnique},
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     mrnumber = {3991897},
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Toby Gee; Olivier Taïbi. Arthur’s multiplicity formula for $\protect \mathbf{GSp}_4$ and restriction to $\protect \mathbf{Sp}_4$. Journal de l’École polytechnique — Mathématiques, Tome 6 (2019), pp. 469-535. doi : 10.5802/jep.99. https://jep.centre-mersenne.org/articles/10.5802/jep.99/

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