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SUMMARY:Finite Singular Orbit Modules for Algebraic Groups - Aluna Rizzoli
 \, Imperial College London
DTSTART:20191108T150000Z
DTEND:20191108T160000Z
UID:TALK131098@talks.cam.ac.uk
CONTACT:Liam Jolliffe
DESCRIPTION:Building on the classification of modules for algebraic groups
  with finitely many orbits on subspaces\, we determine all irreducible mod
 ules for simple algebraic groups that are orthogonal and have finitely man
 y orbits on singular 1-spaces. This question is naturally connected with t
 he problem of finding for which pairs of subgroups H\,K of an algebraic gr
 oup 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
 .
LOCATION:CMS\, MR13
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