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 $p\geq \dim V$.

Authors

Wei Zhang

Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139