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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

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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