2021/05/04 by Aluna Rizzoli, Rizzoli, Aluna
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR)
paper · pdf · doi:10.48550/arxiv.2105.01431
openalex publication_date 2021/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This is the author's second paper treating the double coset problem for classical groups. Let G be an algebraic group over an algebraically closed field K. The double coset problem consists of classifying the pairs H,J of closed connected subgroups of G with finitely many (H,J)-double cosets in G. The critical setup occurs when one of H,J, say H, is reductive, and J is a parabolic subgroup. Assume that G is a classical group, H is simple and J is a maximal parabolic Pk, the stabilizer of a totally singular k-space. Then most candidates have k=1 or k=2. The case k=1 was solved in a previous paper and here we deal with k=2. We solve this case by determining all faithful irreducible self-dual H-modules V, such that H has finitely may orbits on totally singular 2-spaces of V.