The endoscopic fundamental lemma for unitary Friedberg-Jacquet periods

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