Geodesic
Degeneration of Horospheres in Spherical Homogeneous Spaces
Funkcionalʹnyj analiz i ego priloženiâ, Tome 52 (2018) no. 2, pp. 3-14.

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Horospheres for an action of a semisimple algebraic group $G$ on an affine variety $X$ are the generic orbits of a maximal unipotent subgroup $U\subset G$ 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.
Mots-clés : semisimple Lie group
Keywords: homogeneous space, horosphere, spherical variety, symmetric space. 
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E. B. Vinberg; S. G. Gindikin. Degeneration of Horospheres in Spherical Homogeneous Spaces. Funkcionalʹnyj analiz i ego priloženiâ, Tome 52 (2018) no. 2, pp. 3-14. http://geodesic.mathdoc.fr/item/FAA_2018_52_2_a0/

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