Informal Friday Seminar: Liu -- The Brylinski-Kostant filtration

I will talk about the Brylinski-Kostant filtration of weight spaces of simple modules 
of a semi-simple complex Lie algebra (everything is considered to be finite 
dimensional), which was introduced by Ranee Kathryn Brylinski in 1989, using the action 
of a principal nilpotent element. She proved that the "jump polynomial" of this 
filtration equals the corresponding Lusztig's q-polynomial, which also equals certain 
Kazhdan-Lusztig polynomial of the affine Weyl group (up to some shifts of degrees). I 
will start from the definition of a principal nilpotent element of a semi-simple 
complex Lie algebra, but basic knowledge of Lie algebras is necessary for this talk.