A Classification of Certain Finite Double Coset Collections in the Classical Groups
W. Ethan Duckworth
Abstract
Let G be a classical algebraic group, X a maximal rank reductive subgroup and P a parabolic subgroup. This paper classifies when X/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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