Rad HAZU, Matematičke znanosti, Vol. 28 (2024), 353-403.

SÉRIES DISCRÈTES DES ESPACES SYMÉTRIQUES ET PAQUETS D'ARTHUR

Colette Moeglin and David Renard

Centre de Mathématiques Laurent Schwartz, Ecole Polytechnique, Palaiseau, France
e-mail: david.renard@polytechnique.edu

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

2020 Mathematics Subject Classification.   22E50, 11F67.

Key words and phrases.   Discrete spectrum, symmetric spaces, Arthur parameters.

DOI: https://doi.org/10.21857/moxpjhzvwm

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