Visual limits of maximal flats in symmetric spaces and Euclidean buildings

Thomas Haettel

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arXiv · 1206.1227

Visual limits of maximal flats in symmetric spaces and Euclidean buildings

Thomas Haettel

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Abstract

Let X be a symmetric space of non-compact type or a locally finite, strongly transitive Euclidean building, and let B 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 B: 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, 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 surprising algebraic restrictions that occur.

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BibTeX RIS

Thomas Haettel. 2014-03-14. Visual limits of maximal flats in symmetric spaces and Euclidean buildings. https://arxiv.org/abs/1206.1227

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