IISER MOHALI

Abstract: The Brylinski-Kostant filtration on a representation of a finite-dimensional semisimple Lie algebra has interpretations in terms of the algebra, geometry and combinatorics of the representation. Its extension to affine Lie algebras was first studied by Slofstra. In this talk, we construct a Poincare-Birkhoff-Witt type basis for the dominant weight spaces of the basic representation of affine Lie algebras of type A,D, and E, which is compatible with the affine Brylinski filtration. Our result relies on the seminal work of Arakawa which relates representations of affine Kac-Moody algebras to the representations of W-algebras via the Drinfeld-Sokolov reduction functor.