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

2003/09/27 by William Duckworth, W. Ethan Duckworth, Duckworth, W. Ethan
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #math.GR

paper · pdf · doi:10.48550/arxiv.math/0309446

14 pages

arxiv created 2003/09/27 · openalex publication_date 2003/09/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Infiniteness of Double Coset Collections in Algebraic Groups
• Modules for algebraic groups with finitely many orbits on totally singular 2-spaces
• Presentations of parabolics in some elementary Chevalley-Demazure groups
• Finite Singular Orbit Modules for Algebraic Groups
• On multiplication of double cosets for \GL(∞) over a finite field