Simple compactifications and polar decomposition of homogeneous real spherical spaces

Friedrich Knop; Bernhard Krötz; Eitan Sayag; Henrik Schlichtkrull

doi:10.1007/s00029-014-0174-6

Simple compactifications and polar decomposition of homogeneous real spherical spaces

Friedrich Knop, Bernhard Krötz, Eitan Sayag, Henrik Schlichtkrull

Department of Mathematics

Ben-Gurion University of the Negev

Research output: Contribution to journal › Article › peer-review

Abstract

Let Z be an algebraic homogeneous space $$Z=G/H$$Z=G/H attached to real reductive Lie group $$G$$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.

Original language	American English
Pages (from-to)	1071-1097
Number of pages	27
Journal	Selecta Mathematica, New Series
Volume	21
Issue number	3
DOIs	https://doi.org/10.1007/s00029-014-0174-6
State	Published - 23 Dec 2015

Keywords

Compactification
Polar decomposition
Spherical spaces

All Science Journal Classification (ASJC) codes

General Mathematics
General Physics and Astronomy

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10.1007/s00029-014-0174-6

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AU - Knop, Friedrich

AU - Krötz, Bernhard

AU - Sayag, Eitan

AU - Schlichtkrull, Henrik

PY - 2015/12/23

Y1 - 2015/12/23

N2 - Let Z be an algebraic homogeneous space $$Z=G/H$$Z=G/H attached to real reductive Lie group $$G$$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.

AB - Let Z be an algebraic homogeneous space $$Z=G/H$$Z=G/H attached to real reductive Lie group $$G$$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.

KW - Compactification

KW - Polar decomposition

KW - Spherical spaces

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U2 - 10.1007/s00029-014-0174-6

DO - 10.1007/s00029-014-0174-6

M3 - Article

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VL - 21

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EP - 1097

JO - Selecta Mathematica, New Series

JF - Selecta Mathematica, New Series

IS - 3

ER -

Simple compactifications and polar decomposition of homogeneous real spherical spaces

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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