Finite Singular Orbit Modules for Algebraic Groups

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• Aluna Rizzoli, Imperial College London
• Friday 08 November 2019, 15:00-16:00
• CMS, MR13.

If you have a question about this talk, please contact Liam Jolliffe.

Building on the classification of modules for algebraic groups with finitely many orbits on subspaces, we determine all irreducible modules for simple algebraic groups that are orthogonal and have finitely many orbits on singular 1-spaces. 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. We provide a solution to the question when K is a maximal parabolic subgroup P_1 of a classical group SO_n. We find an interesting range of new examples ranging from a 5-dimensional module for SL_2 to the spin module for B_6 in characteristic 2.

This talk is part of the Junior Algebra and Number Theory seminar series.

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