Séries discrètes des espaces symétriques et paquets d'Arthur

Abstract

We check Sakellaridis-Venkatesh conjectures giving a description of the discrete spectrum of a spherical variety $\mathcal{X}=G/H$ in the Langlands-Arthur formalism when $G$ is a classical real group and $\mathcal{X}$ is a symmetric space. Then, we compute explicitly the representations in the relevant Arthur paquets which appear in the discrete spectrum, and we establish some multiplicity one results.

arXiv commentV2, 38 pages, in French, 2 tables