Speaker
Description
We investigate the representation theory of simple affine vertex algebra $L_k(\mathfrak{g})$ at special non-admissible levels $k_n=-\frac{2n+1}{2}$ for $\mathfrak{g} = \mathfrak{sl}_{2n}$. We classify irreducible $L_{k_n}(\mathfrak{sl}_{2n})$-modules in category $KL_{k_n}(\mathfrak{sl}_{2n})$ and prove that $KL_{k_n}(\mathfrak{sl}_{2n})$ is a semi-simple, rigid braided tensor category.
In addition, we present a new method for proving simplicity of quotients of universal affine vertex algebras $V^{k_n}(\mathfrak{sl}_{2n})$. We use this result to prove that in the case $n=3$ a maximal ideal is generated by one singular vector of conformal weight 4. As a byproduct, we classify irreducible modules in the category $\mathcal{O}$ for $L_{-7/2}(\mathfrak{sl}_6)$.
The talk is based on joint papers with D. Adamović, T. Creutzig and O. Perše.
