A local trace formula for the Gan-Gross-Prasad conjecture for unitary groups: the Archimedean case - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Asterisque Année : 2020

A local trace formula for the Gan-Gross-Prasad conjecture for unitary groups: the Archimedean case

Résumé

In this paper, we prove, following earlier work of Waldspurger \cite{Wa1}, \cite{Wa4} a sort of local relative trace formula which is related to the local Gan-Gross-Prasad conjecture for unitary groups over a local field $F$ of characteristic zero. As a consequence, we obtain a geometric formula for certain multiplicities $m(\pi)$ appearing in this conjecture and deduce from it a weak form of the local Gan-Gross-Prasad conjecture (multiplicity one in tempered L-packets). These results were already known over $p$-adic fields \cite{Beu1} and thus are only new when $F=\mathbb{R}$.
Fichier principal
Vignette du fichier
GGPreal_version definitive-5.pdf (2.47 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-01941347 , version 1 (30-11-2018)

Identifiants

Citer

Raphaël Beuzart-Plessis. A local trace formula for the Gan-Gross-Prasad conjecture for unitary groups: the Archimedean case. Asterisque, 2020, 418, ⟨10.24033/ast.1120⟩. ⟨hal-01941347⟩
110 Consultations
133 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More