VISUAL LIMITS OF MAXIMAL FLATS IN SYMMETRIC SPACES AND EUCLIDEAN BUILDINGS
Identifieur interne : 000020 ( France/Analysis ); précédent : 000019; suivant : 000021VISUAL LIMITS OF MAXIMAL FLATS IN SYMMETRIC SPACES AND EUCLIDEAN BUILDINGS
Auteurs : T. Haettel [France]Source :
- Transformation Groups [ 1083-4362 ] ; 2013-12-01.
Abstract
Abstract: Let X be a Riemannian symmetric space of non-compact type or a locally finite, strongly transitive Euclidean building, and let ∂∞X denote the geodesic boundary of X. We reduce the study of visual limits of maximal flats in X to the study of limits of apartments in the spherical building ∂∞X: this defines a natural, geometric compactification of the space of maximal flats of X. We then completely determine the possible degenerations of apartments when X is of rank 1 or associated to a classical group of rank 2 or to PGL(4). In particular, we exhibit remarkable behaviours of visual limits of maximal flats in various symmetric spaces of small rank and the surprising algebraic restrictions that occur.
Url:
DOI: 10.1007/s00031-013-9248-3
Affiliations:
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