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

Gee, Toby; Taïbi, Olivier

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

Nous donnons une preuve de la classification des représentations automorphes discrètes de ${\mathbf{GSp}}_4$ expliquée dans [Art04], ainsi que de la compatibilité avec les correspondances de Langlands locales pour ${\mathbf{GSp}}_4$ et ${\mathbf{Sp}}_4$.

We prove the classification of discrete automorphic representations of ${\mathbf{GSp}}_4$ explained in [Art04], as well as a compatibility between the local Langlands correspondences for ${\mathbf{GSp}}_4$ and ${\mathbf{Sp}}_4$.

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

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