Margulis, Gregory Existence of compact quotients of homogeneous spaces, measurably proper actions, and decay of matrix coefficients. (English) Zbl 0892.22009 Bull. Soc. Math. Fr. 125, No. 3, 447-456 (1997). Let \(G\) be a Lie group and \(H\) a closed subgroup of \(G\). If \(H\) is noncompact it is not known when \(G/H\) has a compact quotient (even for semisimple \(G\)). There are several criteria, however, to prove that a given \(G/H\) has no compact quotients. These criteria are based on considerations from topology, ergodic theory and the theory of linear groups. In this paper, the author gives a new criterion based on the study of the restriction to \(H\) of matrix coefficients of unitary representations of \(G\). Using this criterion, new examples of homogeneous spaces \(G/H\) without compact quotients can be generated. Reviewer: Govindan Rangarajan (Bangalore) Cited in 11 Documents MSC: 22E40 Discrete subgroups of Lie groups 22E46 Semisimple Lie groups and their representations 53C30 Differential geometry of homogeneous manifolds 57S30 Discontinuous groups of transformations Keywords:compact quotients; homogeneous spaces; unitary representations PDFBibTeX XMLCite \textit{G. Margulis}, Bull. Soc. Math. Fr. 125, No. 3, 447--456 (1997; Zbl 0892.22009) Full Text: DOI Numdam EuDML References: [1] KOBAYASHI (T.) . - Discontinuous groups and Clifford-Klein forms on pseudoriemannian homogeneous manifolds , in “Algebraic and analytic methods in representation theory”. - B. Orsted and H. Schlichtkrull eds, Perspectives in Mathematics, vol. 17, Academic Press, p. 99-165. MR 97g:53061 | Zbl 0899.43005 · Zbl 0899.43005 [2] LABOURIE (F.) . - Quelques résultats récents sur les espaces localement homogènes compacts , in “Manifolds and Geometry”, actes d’un colloque (Pise 1993 ) en l’honneur d’Eugenio Calabi. - P. de Bartolomeis, F. Tricerri and E. Vesentini eds, Symposia Mathematica, vol. XXXVI, Cambridge University Press 1996 . Zbl 0861.53053 · Zbl 0861.53053 [3] OH (H.) . - Representations with minimal decay of matrix coefficients and tempered subgroups , Preprint. · Zbl 0917.22008 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.