The global Gan--Gross--Prasad conjecture for Fourier--Jacobi periods on unitary groups II: Comparison of the relative trace formulae

TL;DR

This paper compares two relative trace formulae to advance the proof of the Gan--Gross--Prasad conjecture for Fourier--Jacobi periods on unitary groups, contributing to a broader program of establishing deep automorphic period conjectures.

Contribution

It provides a detailed comparison of two key relative trace formulae, facilitating progress towards the conjecture's proof for unitary groups.

Findings

Successful comparison of the two trace formulae

Establishment of foundational identities for the conjecture

Progress towards the proof of the Gan--Gross--Prasad conjecture

Abstract

This is the second 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. The goal of this second paper is to compare the two relative trace formulae.