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The global Gan-Gross-Prasad conjecture for unitary groups: the endoscopic case
Publications Mathématiques de l'IHÉS, Volume 135 (2022), pp. 183-336
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In this paper, we prove the Gan-Gross-Prasad conjecture and the Ichino-Ikeda conjecture for unitary groups U n ×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.

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DOI: 10.1007/s10240-021-00129-1

Raphaël Beuzart-Plessis 1; Pierre-Henri Chaudouard 1; Michał Zydor 1

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

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