Abstract
Let G be a connected, reductive, algebraic group on an algebraically closed field k of characteristic zero. Let H be aspherical subgroup of G, i.e. H is a closed subgroup of G such that every Borel subgroup of G operates on G/H with an open orbit.
It is shown that for a spherical subgroup H, the homogeneous space G/H is a deformation of a homogeneous space G/H0, where H0 contains a maximal unipotent subgroup of G (such a H0 is spherical). It is also shown that every Borel subgroup of G has a finite number of orbits in G/H.
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Brion, M. Quelques proprietes des espaces homogenes spheriques. Manuscripta Math 55, 191–198 (1986). https://doi.org/10.1007/BF01168684
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DOI: https://doi.org/10.1007/BF01168684