Isolation of cuspidal spectrum, with application to the Gan–Gross–Prasad conjecture

Pages 519-584 from Volume 194 (2021), Issue 2 by Raphaël Beuzart-Plessis, Yifeng Liu, Wei Zhang, Xinwen Zhu

Abstract

We introduce a new technique for isolating components on the spectral side of the trace formula. By applying it to the Jacquet–Rallis relative trace formula, we complete the proof of the global Gan–Gross–Prasad conjecture and its refinement Ichino–Ikeda conjecture for $\mathrm {U}(n)\times \mathrm {U}(n+1)$ in the stable case.

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Keywords
, , , ,
Mathematical Subject Classification
Primary: , ,
DOI
https://www.doi.org/10.4007/annals.2021.194.2.5
MR
4298750
zbMATH
7395719
Milestones
Received: 17 January 2020
Revised: 17 May 2021
Accepted: 21 May 2021
Published online: 13 August 2021

Authors

Raphaël Beuzart-Plessis

Département de Mathématiques, Université d'Aix-Marseille, CNRS, I2M, Marseille, France

Yifeng Liu

Institute for Advanced Study in Mathematics, Zhejiang University, Hangzhou, China

Wei Zhang

Department of Mathematics, Massachusetts Institute of Technology, Cambridge MA, United States

Xinwen Zhu

Division of Physics, Mathematics and Astronomy, California Institute of Technology, Pasadena CA, United States