Simple compactifications and polar decomposition of homogeneous real spherical spaces

• Friedrich Knop ^[4] ; Bernhard Krötz ^[1] ; Eitan Sayag ^[2] ; Henrik Schlichtkrull ^[3]
  1. [1] University of Paderborn

     University of Paderborn

     Kreis Paderborn, Alemania

     
  2. [2] Ben-Gurion University of the Negev

     Ben-Gurion University of the Negev

     Israel

     
  3. [3] University of Copenhagen

     University of Copenhagen

     Dinamarca

     
  4. [4] Emmy-Noether-Zentrum

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 21, Nº. 3, 2015, págs. 1071-1097
• Idioma: inglés
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• Resumen

  • Let ZZ be an algebraic homogeneous space Z=G/HZ=G/H attached to real reductive Lie group GG . We assume that ZZ is real spherical, i.e., minimal parabolic subgroups have open orbits on ZZ . For such spaces, we investigate their large scale geometry and provide a polar decomposition. This is obtained from the existence of simple compactifications of ZZ which is established in this paper.