Representation theory and duality properties of some affine W-algebras

Abstract: One of the most important families of vertex algebras are affine vertex algebras and their associated $\mathcal{W}$-algebras, which are connected to various aspects of geometry and physics. Among the simplest examples of $\mathcal{W}$-algebras is the Bershadsky-Polyakov vertex algebra $\mathcal{W}^k(\mathfrak{g}, f_{min})$, associated to $\mathfrak{g} = sl(3)$ and the minimal nilpotent element $f_{min}$. In this talk we are particularly interested in the Bershadsky-Polyakov algebra $\mathcal W_k$ at positive integer levels, for which we obtain a complete classification of irreducible modules. In the case $k=1$, we show that this vertex algebra has a Kazama-Suzuki-type dual isomorphic to the simple affine vertex superalgebra $L_{k'} (osp(1 \vert 2))$ for $k'=-5/4$. This is joint work with D. Adamovic.

Mathematics

Audience: researchers in the topic

European Quantum Algebra Lectures (EQuAL)

Series comments: EQuAL is an online seminar series on quantum algebra and related topics such as topological and conformal field theory, operator algebra, representation theory, quantum topology, etc. sites.google.com/view/equalseminar/home