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

Beuzart-Plessis, Raphaël; Chaudouard, Pierre-Henri; Zydor, Michał

doi:10.1007/s10240-021-00129-1

Article

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

Beuzart-Plessis, Raphaël ; Chaudouard, Pierre-Henri ; Zydor, Michał

Publications Mathématiques de l'IHÉS, Tome 135 (2022), pp. 183-336

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 ∗-regular, 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 introduced by Jacquet-Lapid-Rogawski. 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.

Reçu le : 2021-12-17
Accepté le : 2021-12-20
Première publication : 2022-01-27
Publié le : 2022-06-28

MR Zbl

DOI : 10.1007/s10240-021-00129-1

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     author = {Beuzart-Plessis, Rapha\"el and Chaudouard, Pierre-Henri and Zydor, Micha{\l}},
     title = {The global {Gan-Gross-Prasad} conjecture for unitary groups: the endoscopic case},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {183--336},
     year = {2022},
     publisher = {Springer International Publishing},
     address = {Cham},
     volume = {135},
     doi = {10.1007/s10240-021-00129-1},
     mrnumber = {4426741},
     zbl = {1537.11072},
     language = {en},
     url = {https://www.numdam.org/articles/10.1007/s10240-021-00129-1/}
}

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Beuzart-Plessis, Raphaël; Chaudouard, Pierre-Henri; Zydor, Michał. The global Gan-Gross-Prasad conjecture for unitary groups: the endoscopic case. Publications Mathématiques de l'IHÉS, Tome 135 (2022), pp. 183-336. doi: 10.1007/s10240-021-00129-1

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