Israel Journal of Mathematics

, Volume 218, Issue 1, pp 175–271 | Cite as

Sur la contribution unipotente dans la formule des traces d’Arthur pour les groupes généraux linéaires

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Résumé

Le thème de l’article est l’étude de la partie unipotente de la formule des traces d’Arthur pour un groupe général linéaire. La contribution de l’orbite unipotente régulière ou de ses variantes par blocs est traitée dans un autre article (cf. [10]). Ici on s’intéresse à la contribution des orbites unipotentes simples c’est-à-dire aux orbites de Richardson induites à partir d’un sous-groupe de Levi dont les blocs sont de tailles deux-à-deux distinctes. De manière remarquable, la contribution s’exprime à l’aide d’une intégrale orbitale pondérée globale unipotente. Comme corollaire, on obtient des formules intégrales pour certains coefficients globaux d’Arthur. Cet article comprend également une construction nouvelle des intégrales orbitales pondérées unipotentes locales d’Arthur et un calcul explicite de certaines d’entre elles.

Abstract

The theme of the article is the study of the unipotent part of Arthur’s trace formula for general linear groups. The case of regular (or “regular by blocks”) unipotent orbits has been treated in another paper (cf. [10]). Here we are interested in the contribution of Richardson orbits that are induced by Levi subgroups with two-by-two distinct blocks. In this case, the contribution is remarkably given by a global unipotent weighted orbital integral. As a corollary, we get integral formulas for some of Arthur’s global coefficients. We also present a new construction of Arthur’s local unipotent weighted orbital integral and an explicit computation of some of them.

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© Hebrew University of Jerusalem 2017

Authors and Affiliations

  1. 1.Université Paris Diderot (Paris 7) et Institut Universitaire de FranceInstitut de Mathématiques de Jussieu-Paris Rive Gauche, UMR 7586Paris Cedex 13France

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