ALT

Abstract

Premet conjectured that any (finite) W-algebra has a one-dimensional representation. The goal of this talk is to explain results of the speaker towards this conjecture. We will start giving a sketch of proof for the classical Lie algebras. Then we explain a reduction to rigid nilpotent elements using a parabolic induction functor. Finally, we will explain how using the Brundan-Goodwin-Kleshchev category O one can try to describe one-dimensional representations of W-algebras associated to rigid elements in exceptional Lie algebras.