On Whittaker--Fourier coefficients of automorphic forms on unitary groups: reduction to a local identity

TL;DR

This paper investigates Whittaker--Fourier coefficients of automorphic forms on quasi-split unitary groups, reducing a global conjecture to a local identity via descent methods, advancing understanding in automorphic representation theory.

Contribution

It introduces a reduction of the Ichino--Ikeda conjecture for unitary groups to a local conjecture using descent techniques, providing a new approach in the field.

Findings

Reduction of global conjecture to local identity

Application of descent method in automorphic forms

Framework for future verification of local conjecture

Abstract

We study Whittaker--Fourier coefficients of automorphic forms on a quasi-split unitary group. We reduce the analogue of the Ichino--Ikeda conjectures to a conjectural local statement using the descent method of Ginzburg--Rallis--Soudry.