Int\'egrale orbitale pond\'er\'ee via l'induite de Lusztig-Spaltenstein g\'en\'eralis\'ee

Abstract

In this article, we present two novel approaches to constructing weighted orbital integrals of an inner form of a general linear group. Our method utilizes generalized Lustig-Spaltenstein induction. Furthermore, we will prove that a weighted orbital integral on the Lie algebra constitutes a tempered distribution. We also demonstrate that our new definitions and Arthur's original definition are consistent.