Seminar in Algebra, Lie Theory, and Geometry

Alexey Petukhov

(MPIM Bonn)

"SL(2)-geometry of the flag variety of Sp(4) and sp(4)-modules of finite type"


Date: Fri, April 5, 2013
Time: 11:15
Place: East Hall 8

Abstract: In my talk I will describe a geometry of SL(2)-action on a variety of full isotropic flags in four(five)-dimensional space (it turns out that this variety is a semi-direct product of 3-dimensional projective space and 3-dimensional conic). Then I provide a definition of sp(4)-modules of finite type and show how to reduce the problem of classification of such sp(4)-modules to SL(2)-geometry. At the end I will say some words about problems of SL(2)-action which are very interesting from an algebraic point of view but which I am unable to solve using notions of fundamental group, monodromy along subvariety and similar stuff.