Weil representation and Arithmetic Fundamental Lemma

Abstract

We study a partially linearized version of the relative trace formula for the arithmetic Gan–Gross–Prasad conjecture for the unitary group $\mathrm {U}(V)$. The linear factor in this relative trace formula provides an $\mathrm {SL}_2$-symmetry which allows us to prove by induction the arithmetic fundamental lemma over $\mathbb {Q}_p$ when $p$ is odd and $p\geq \dim V$.