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arXiv · 2007.05601

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

Raphaël Beuzart-Plessis·Pierre-Henri Chaudouard·Michał Zydor
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Abstract

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.

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Raphaël Beuzart-Plessis, Pierre-Henri Chaudouard, Michał Zydor. 2020-07-10. The global Gan-Gross-Prasad conjecture for unitary groups: the endoscopic case. https://arxiv.org/abs/2007.05601

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