Journal of Lie Theory 20 (2010), No. 3, 437--468
Copyright Heldermann Verlag 2010
Compactification de Chabauty des Espaces Symétriques de Type Non Compact
Thomas Haettel
Dép. de Mathématiques, ENS Paris, 45, Rue d'Ulm, 75005 Paris, France
thomas.haettel@ens.fr
The space of closed subgroups of a locally compact topological group is endowed with a natural topology, called the Chabauty topology. Let X be a symmetric space of noncompact type, and G be its group of isometries. The space X identifies with the subspace of maximal compact subgroups of G : taking the closure gives rise to the Chabauty compactification of the symmetric space X. Using simpler arguments than those presented by Y. Guivarc'h, L. Ji and J. C. Taylor [Compactifications of symmetric spaces, Progr. Math. 156 (1998)] we describe the subgroups that appear in the boundary of the compactification, and classify the maximal distal and maximal amenable subgroups of G. We also provide a straightforward identification between the Chabauty compactification and the polyhedral compactification.
Keywords: Compactification, Chabauty, symmetric space, space of subgroup.
MSC: 57S05, 57S20, 57S25
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