This article is cited in 1 paper

Degeneration of Horospheres in Spherical Homogeneous Spaces

E. B. Vinberg^a, S. G. Gindikin<sup>b

a</sup> Lomonosov Moscow State University, Moscow, Russia
^b Rutgers University, Department of Mathematics, Rutgers, USA

Abstract: 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.

Keywords: semisimple Lie group, homogeneous space, horosphere, spherical variety, symmetric space.

UDC: 512.816.4--512.745.2

Received: 22.01.2018

DOI: 10.4213/faa3555

 English version: Functional Analysis and Its Applications, 2018, 52:2, 83–92

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