W-algebras and representations of affine Lie algebras

Abstract: Quantum Hamiltonian reduction associates W-algebras with affine Lie algebras and nilpotent elements. I will discuss inverse constructions and their applications to the representation theory of affine Lie algebras and W-algebras. Starting with the relation between the affine Lie algebra $\widehat{\mathfrak{sl}}_2$ and the Virasoro algebra, I will explain how these constructions yield explicit realizations of irreducible modules. Further examples will involve $\mathfrak{sl}_3$ and subregular W-algebras of type A. The necessary notions from vertex algebra theory will be introduced.

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar