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

W. Ethan Duckworth

paper

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

arXiv:math/0309446

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.

14 pages