Degeneration of Horospheres in Spherical Homogeneous Spaces

Horospheres for an action of a semisimple algebraic group G on an affine variety X are the generic orbits of a maximal unipotent subgroup U ⊂ G or, equivalently, the generic fibers of the categorical quotient of the variety X by the action of U , which is defined by the values of the highest weight...

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Bibliographic Details
Published in:Functional analysis and its applications 2018-04, Vol.52 (2), p.83-92
Main Authors: Vinberg, E. B., Gindikin, S. G.
Format: Article
Language:English
Subjects:
Analysis
Degeneration
Functional Analysis
Mathematics
Mathematics and Statistics
Subgroups
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Summary:Horospheres for an action of a semisimple algebraic group G on an affine variety X are the generic orbits of a maximal unipotent subgroup U ⊂ G or, equivalently, the generic fibers of the categorical quotient of the variety X by the action of U , which is defined by the values of the highest weight functions. The remaining fibers of this quotient (which we call degenerate horospheres) for a certain class of spherical G -varieties containing all simply connected symmetric spaces are studied.
ISSN:0016-2663
1573-8485
DOI:10.1007/s10688-018-0214-7