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


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.


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