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

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

2003-09-27

arxiv.org/abs/math/0309446v1

Mathematics

Group Theory

14 pages

Scientific paper

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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