La formule des traces stable pour le groupe métaplectique: les termes elliptiques

Abstract

Let F be a number field and $\widetilde{\mathrm{Sp}}(2n)$ be the metaplectic covering of Weil of $\mathrm{Sp}(2n, \mathbb{A}_F)$. We stabilize the elliptic semi-simple terms of the genuine part of trace formula for $\widetilde{\mathrm{Sp}}(2n)$, by using the transfer of test functions and the fundamental lemma established in a previous article. We obtain therefore an expression in terms of stable orbital integrals along certain $F$-elliptic classes in $\mathrm{SO}(2n'+1) \times \mathrm{SO}(2n''+1)$, which we call equisingular, for pairs $(n', n'')$ satisfying $n'+n''=n$. A simple formula for the coefficients is also obtained.