The global Gan--Gross--Prasad conjecture for Fourier--Jacobi periods on unitary groups III: Proof of the main theorems

Paul Boisseau; Weixiao Lu; Hang Xue

doi:10.48550/arxiv.2601.01738

The global Gan--Gross--Prasad conjecture for Fourier--Jacobi periods on unitary groups III: Proof of the main theorems

arXiv (Cornell University) 2026 Preprint Open access

Read full text

Authors: Paul Boisseau, Weixiao Lu, Hang Xue

DOI: 10.48550/arxiv.2601.01738

Cited by: 0

Abstract

This is the third and the last of a series of three papers where we prove the Gan--Gross--Prasad conjecture for Fourier--Jacobi periods on unitary groups and an Ichino--Ikeda type refinement. Our strategy is based on the comparison of relative trace formulae formulated by Liu. In this paper, we compute the spectral expansions of these formulae and end the proof of the conjectures via a reduction to the corank zero case.

Fields of Study & Subjects

Advanced Algebra and Geometry Geometry and complex manifolds Quantum chaos and dynamical systems

Publication details

Journal / source: arXiv (Cornell University)
Publication date: 5 January 2026
Document type: Preprint