Abstract
Building on the classification of modules for algebraic groups with finitely many orbits on subspaces [9], we determine all faithful irreducible modules V for a connected simple algebraic group H, such that H≤SO(V) and H has finitely many orbits on singular 1-spaces of V. We do the same for H connected semisimple, and maximal among connected semisimple subgroups. This question is naturally connected with the problem of finding for which pairs of subgroups H,K of an algebraic group G there are finitely many (H,K)-double cosets. This paper provides a solution to the question when K is a maximal parabolic subgroup P1 of a classical group SOn, where P1 is the stabilizer of a singular 1-space. We find an interesting range of new examples, from a 5-dimensional module for A1 in characteristic p>5, to the spin module for B6 when p=2.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.