Resumen de Simple compactifications and polar decomposition of homogeneous real spherical spaces

Friedrich Knop, Bernhard Krötz, Eitan Sayag, Henrik Schlichtkrull

• 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.