This article is cited in 1 paper

Affine spherical homogeneous spaces with good quotient by a maximal unipotent subgroup

R. S. Avdeev

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: For an affine spherical homogeneous space $G/H$ of a connected semisimple algebraic group $G$, we consider the factorization morphism by the action on $G/H$ of a maximal unipotent subgroup of $G$. We prove that this morphism is equidimensional if and only if the weight semigroup of $G/H$ satisfies a simple condition.
Bibliography: 16 titles.

Keywords: algebraic group, homogeneous space, spherical subgroup, equidimensional morphism, semigroup.

UDC: 512.745

MSC: 14L30, 14M27, 14M17

Received: 11.06.2011 and 16.04.2012

DOI: 10.4213/sm7897

 English version: Sbornik: Mathematics, 2012, 203:11, 1535–1552

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