Abstract
Let \(Z\) be an algebraic homogeneous space \(Z=G/H\) attached to real reductive Lie group \(G\). We assume that \(Z\) is real spherical, i.e., minimal parabolic subgroups have open orbits on \(Z\). For such spaces, we investigate their large scale geometry and provide a polar decomposition. This is obtained from the existence of simple compactifications of \(Z\) which is established in this paper.
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We thank the anonymous referee for useful suggestions which led to an improvement of our paper.
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B. Krötz was supported by ERC Advanced Investigators Grant HARG 268105. E. Sayag was partially supported by ISF 1138/10 and ERC 291612.
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Knop, F., Krötz, B., Sayag, E. et al. Simple compactifications and polar decomposition of homogeneous real spherical spaces. Sel. Math. New Ser. 21, 1071–1097 (2015). https://doi.org/10.1007/s00029-014-0174-6
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DOI: https://doi.org/10.1007/s00029-014-0174-6