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.
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HAETTEL, T. VISUAL LIMITS OF MAXIMAL FLATS IN SYMMETRIC SPACES AND EUCLIDEAN BUILDINGS. Transformation Groups 18, 1055–1089 (2013). https://doi.org/10.1007/s00031-013-9248-3
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DOI: https://doi.org/10.1007/s00031-013-9248-3