Algebra Seminar: Ridout -- Admissible level affine vertex operator algebras

David Ridout (University of Melbourne)

Friday 8 April, 12-1pm, Place: Carslaw 375

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 of sl(2).