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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68693Let $G$ 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 pagesGroup TheoryA Classification of Certain Finite Double Coset Collections in the Classical Groupstext