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A Classification of Certain Finite Double Coset Collections in the Classical Groups

W. Ethan Duckworth
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Abstract

Let $G$ be a classical algebraic group, $X$ a maximal rank reductive subgroup and $P$ a parabolic subgroup. This paper classifies when $X\G/P$ 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 which involves root systems.

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W. Ethan Duckworth. 2003-09-27. A Classification of Certain Finite Double Coset Collections in the Classical Groups. https://arxiv.org/abs/math/0309446

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