# David Ridout (University of Melbourne)

## Admissible level affine vertex operator algebras

Affine Kac-Moody algebras have a central element whose eigenvalue, when acting on modules, is called the level. For every (non-critical) level, there is a highest-weight module that admits the structure of a vertex operator algebra (VOA). For certain special levels, called admissible levels (by some), this VOA need not be simple. Physicists are interested in the representation theory of the simple quotient of the admissible level VOAs: for example, the non-negative integer levels describe the well-understood Wess-Zumino-Witten models of string theory. I shall discuss some recent advances concerning the other admissible levels, which are rather less well-understood, restricting to the affine Kac-Moody algebra $$\widehat{\mathfrak{sl}}(2)$$.