Type: Seminar

Distribution: World

CalTitle1: Liu - The Brylinski-Kostant filtration

Auth: romanova@10.17.124.151 (arom8272) in SMS-WASM

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.