
Journal of Lie Theory 22 (2012), No. 2, 505522 Copyright Heldermann Verlag 2012 Spherical Subgroups and Double Coset Varieties Artem Anisimov Dept. of Higher Algebra, Faculty of Mechanics and Mathematics, Lomonosov State University, Leninskie Gory 1 / GSP1, Moscow 119991, Russia aanisimov@inbox.ru [Abstractpdf] \def\dcosets #1#2#3 {#1 \hskip1pt \backslash \hskip3pt \backslash \hskip0.8pt{#2}\hskip1pt\slash\hskip3pt\slash #3 \hskip1pt} Let $G$ be a connected reductive algebraic group, $H \subset G$ a reductive subgroup and $T \subset G$ a maximal torus. It is well known that if charactersitic of the ground field is zero, then the homogeneous space $G/H$ is a smooth affine variety, but never an affine space. The situation changes when one passes to double coset varieties $\dcosets{F}{G}{H}$. In this paper we consider the case of $G$ classical and $H$ connected spherical and prove that either the double coset variety $\dcosets{T}{G}{H}$ is singular, or it is an affine space. We also list all pairs $H \subset G$ such that $\dcosets{T}{G}{H}$ is an affine space. Keywords: Double coset varieties. MSC: 14L30,14M17 [ Fulltextpdf (315 KB)] for subscribers only. 