Category O via Zastava spaces

Abstract: In my talk I will recall basic results about category O for finite-dimensional and affine Lie algebras - such as Kazhdan-Lusztig conjecture, Jantzen conjecture etc. I will then describe a new geometric approach to proving these conjectures via so called Zastava spaces. developed in my recent paper with Finkelberg and Nakajima. In that paper we give a new proof of the Kazhdan-Lusztig conjecture for semi-simple Lie algebras, I will describe how it should be possible to extend this to Jantzen conjectures and to the affine case.

mathematical physicsalgebraic geometrycategory theoryrepresentation theory

Audience: researchers in the topic

UMass Amherst Representation theory seminar