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 $\mathrm{SO}(2n^{\prime }+1)\times \mathrm{SO}(2n^{\prime \prime }+1)$, which we call equisingular, for pairs $(n^{\prime },n^{\prime \prime })$ satisfying $n^{\prime }+n^{\prime \prime }=n$. A simple formula for the coefficients is also obtained.

70 pages, in French, with various corrections

References in corpus (2)

• Transfert d'intégrales orbitales pour le groupe métaplectique
• Le lemme fondamental pondéré pour le groupe métaplectique