AST418 - A local trace formula for the Gan-Gross-Prasad conjecture for unitary groups: the archimedean case

Abstract

In this paper, we prove, following earlier work of Waldspurger \cite{Wa1}, \cite{Wa4} a sort of local relative trace formula which is related to the local Gan-Gross-Prasad conjecture for unitary groups over a local field $F$ of characteristic zero. As a consequence, we obtain a geometric formula for certain multiplicities $m(\pi)$ appearing in this conjecture and deduce from it a weak form of the local Gan-Gross-Prasad conjecture (multiplicity one in tempered L-packets). These results were already known over $p$-adic fields \cite{Beu1} and thus are only new when $F=\mathbb{R}$.