Stable spectrum for pseudo-Riemannian locally symmetric spaces

Fanny Kassel; Toshiyuki Kobayashi

doi:10.1016/j.crma.2010.11.023

Group Theory/Harmonic Analysis

Stable spectrum for pseudo-Riemannian locally symmetric spaces
[Spectre stable pour les variétés pseudo-riemanniennes localement symétriques]

Présenté par : Michèle Vergne

Fanny Kassel ¹ ; Toshiyuki Kobayashi ²

¹ Department of Mathematics, University of Chicago, 5734 South University Avenue, Chicago, IL 60637, USA
² Graduate School of Mathematical Sciences, IPMU, The University of Tokyo, 3-8-1 Komaba, Tokyo, 153-8914 Japan

Comptes Rendus. Mathématique, Volume 349 (2011) no. 1-2, pp. 29-33.

Résumé
Abstract

Soit $X = G / H$ un espace symétrique réductif vérifiant $rang G / H = rang K / K \cap H$ , où K (resp. $K \cap H$ ) est un sous-groupe compact maximal de G (resp. de H). Nous étudions le spectre discret de certaines formes de Clifford–Klein $Γ \ X$ , où Γ est un sous-groupe discret de G agissant librement et proprement sur X : nous construisons un ensemble infini de valeurs propres pour les opérateurs différentiels « intrinsèques » sur $Γ \ X$ , et cet ensemble est stable par petites déformations de Γ dans G.

Let $X = G / H$ be a reductive symmetric space with $rank G / H = rank K / K \cap H$ , where K (resp. $K \cap H$ ) is a maximal compact subgroup of G (resp. of H). We investigate the discrete spectrum of certain Clifford–Klein forms $Γ \ X$ , where Γ is a discrete subgroup of G acting properly discontinuously and freely on X: we construct an infinite set of joint eigenvalues for “intrisic” differential operators on $Γ \ X$ , and this set is stable under small deformations of Γ in G.

Reçu le : 2010-06-23
Accepté le : 2010-11-22
Publié le : 2010-12-24

DOI : 10.1016/j.crma.2010.11.023

Affiliations des auteurs :

Fanny Kassel ¹ ; Toshiyuki Kobayashi ²

¹ Department of Mathematics, University of Chicago, 5734 South University Avenue, Chicago, IL 60637, USA
² Graduate School of Mathematical Sciences, IPMU, The University of Tokyo, 3-8-1 Komaba, Tokyo, 153-8914 Japan

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     author = {Fanny Kassel and Toshiyuki Kobayashi},
     title = {Stable spectrum for {pseudo-Riemannian} locally symmetric spaces},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {29--33},
     publisher = {Elsevier},
     volume = {349},
     number = {1-2},
     year = {2011},
     doi = {10.1016/j.crma.2010.11.023},
     language = {en},
}

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Fanny Kassel; Toshiyuki Kobayashi. Stable spectrum for pseudo-Riemannian locally symmetric spaces. Comptes Rendus. Mathématique, Volume 349 (2011) no. 1-2, pp. 29-33. doi : 10.1016/j.crma.2010.11.023. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.11.023/

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