The endoscopic fundamental lemma for unitary Friedberg–Jacquet periods

Abstract

We prove the endoscopic fundamental lemma for the Lie algebra of the symmetric variety $\mathrm{U}(2n)/\mathrm{U}(n)\times \mathrm{U}(n)$, where $\mathrm{U}(n)$ denotes a unitary group of rank $n$. This is the first major step in the stabilization of the relative trace formula associated to the $\mathrm{U}(n)\times \mathrm{U}(n)$-periods of automorphic forms on $\mathrm{U}(2n)$.