S\'eries discr\`etes des espaces sym\'etriques et paquets d'Arthur

TL;DR

This paper verifies conjectures describing the discrete spectrum of certain symmetric spaces for classical real groups, explicitly computes relevant Arthur packets, and proves some multiplicity one results.

Contribution

It confirms Sakellaridis-Venkatesh conjectures for classical real groups and symmetric spaces, providing explicit computations of Arthur packets and new multiplicity one theorems.

Findings

Verification of Sakellaridis-Venkatesh conjectures for classical groups

Explicit computation of Arthur packets in the discrete spectrum

Establishment of multiplicity one results

Abstract

We check Sakellaridis-Venkatesh conjectures giving a description of the discrete spectrum of a spherical variety $\mathscr{X}=G/H$ in the Langlands-Arthur formalism when $G$ is a classical real group and $\mathscr{X}$ 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.