Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Lie Theory 22 (2012), No. 2, 505--522Copyright 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 / GSP-1, Moscow 119991, Russia aanisimov@inbox.ru [Abstract-pdf] \def\dcosets #1#2#3 {#1 \hskip-1pt \backslash \hskip-3pt \backslash \hskip-0.8pt{#2}\hskip-1pt\slash\hskip-3pt\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 [ Fulltext-pdf  (315  KB)] for subscribers only.