Relative trace formulae toward Bessel and Fourier–Jacobi periods on unitary groups

Abstract

We propose an approach, via relative trace formulae, toward the global restriction problem involving Bessel or Fourier–Jacobi periods on unitary groups U[subscript n] × U[subscript m], generalizing the work of Jacquet–Rallis for m = n − 1 (which is a Bessel period). In particular, when m = 0, we recover a relative trace formula proposed by Flicker concerning Kloosterman/Fourier integrals on quasi-split unitary groups. As evidences for our approach, we prove the vanishing part of the fundamental lemmas in all cases, and the full lemma for U[subscript n] × U[subscript n].