Sur la contribution unipotente dans la formule des traces d'Arthur pour les groupes g\'en\'eraux lin\'eaires

摘要

The theme of the article is the study of the unipotent part of Arthur's traceformula for general linear groups. The case of regular (or "regular by blocks")unipotent orbits has been essentially done in a previous paper. Here we areinterested by the contribution of Richardson orbits that are induced by Levisubgroups with two-by-two distinct blocks. In this case, the contribution isremarkably given by a global unipotent weighted orbital integral. As acorollary, we get integral formulas for some of Arthur's global coefficients.We also present a new construction of Arthur's local unipotent weighted orbitalintegral.