Whittaker–Shintani Functions for Fourier–Jacobi Models on Unitary Groups

Abstract We state and prove a formula for the Whittaker–Shintani functions associated to Fourier–Jacobi models for $p$-adic unitary groups and general linear groups. These generalized spherical functions play a fundamental role in the proof of the Gan–Gross–Prasad conjecture for Fourier–Jacobi models. As an application, we prove the unramified Ichino–Ikeda conjecture.