The global Gan-Gross-Prasad conjecture for unitary groups: the endoscopic case - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2022

The global Gan-Gross-Prasad conjecture for unitary groups: the endoscopic case

Résumé

In this paper, we prove the Gan-Gross-Prasad conjecture and the Ichino-Ikeda conjecture for unitary groups $U_n\times U_{n+1}$ in all the endoscopic cases. Our main technical innovation is the computation of the contributions of certain cuspidal data, called $*$-generic, to the Jacquet-Rallis trace formula for linear groups. We offer two different computations of these contributions: one, based on truncation, is expressed in terms of regularized Rankin-Selberg periods of Eisenstein series and Flicker-Rallis intertwining periods. The other, built upon Zeta integrals, is expressed in terms of functionals on the Whittaker model. A direct proof of the equality between the two expressions is also given. Finally several useful auxiliary results about the spectral expansion of the Jacquet-Rallis trace formula are provided.
Fichier principal
Vignette du fichier
2007.05601.pdf (1.19 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-02989495 , version 1 (09-01-2024)

Identifiants

Citer

Raphaël Beuzart-Plessis, Pierre-Henri Chaudouard, Michał Zydor. The global Gan-Gross-Prasad conjecture for unitary groups: the endoscopic case. 2024. ⟨hal-02989495⟩
128 Consultations
3 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More