A double coset problem for classical groups

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 self-dual and have finitely many orbits on totally singular k-spaces (k=1 or k=2). This question is naturally connected with the problem of finding for which pairs of subgroups H,J of an algebraic group G there are finitely many (H,J)-double cosets. We provide a solution to the question when J is a maximal parabolic subgroup P_k of a classical group.

Date and Venue

Start Date
Online Zoom meeting
End Date


Aluna Rizzoli

Speaker's Institution

Imperial College London



Algebra, Combinatorics and Number Theory