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A CLASSIFICATION OF CERTAIN FINITE DOUBLE COSET COLLECTIONS IN THE CLASSICAL GROUPS
Published online by Cambridge University Press: 19 October 2004
Abstract
Let $G$ be a classical algebraic group, $X$ a maximal rank reductive subgroup and $P$ a parabolic subgroup. This paper classifies when $X\backslash G/P$ is finite. Finiteness is proven using geometric arguments about the action of $X$ on subspaces of the natural module for $G$. Infiniteness is proven using a dimension criterion that involves root systems.
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- © The London Mathematical Society 2004
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