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Simple compactifications and polar decomposition of homogeneous real spherical spaces

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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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Acknowledgments

We thank the anonymous referee for useful suggestions which led to an improvement of our paper.

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Authors and Affiliations

  1. Department Mathematik, Emmy-Noether-Zentrum, FAU Erlangen-Nürnberg, Cauerstr. 11, 91058, Erlangen, Germany

    Friedrich Knop

  2. Institut für Mathematik, Universität Paderborn, Warburger Straße 100, 33098, Paderborn, Germany

    Bernhard Krötz

  3. Department of Mathematics, Ben Gurion University of the Negev, P.O.B. 653, 84105, Beersheba, Israel

    Eitan Sayag

  4. Department of Mathematics, University of Copenhagen, Universitetsparken 5, 2100, Copenhagen Ø, Denmark

    Henrik Schlichtkrull

Authors
  1. Friedrich Knop
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  2. Bernhard Krötz
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  3. Eitan Sayag
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  4. Henrik Schlichtkrull
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Corresponding author

Correspondence to Henrik Schlichtkrull.

Additional information

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

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