Vertex Operator Algebras Associated to Admissible Representations of

Abstract:

The Kac-Wakimoto admissible modules for $\hat{sl}_2$ are studied from the point of view of vertex operator algebras. It is shown that the vertex operator algebra L(l,0) associated to irreducible highest weight modules at admissible level $l={p\over q}-2$ is not rational if l is not a positive integer. However, a suitable change of the Virasoro algebra makes L(l,0) a rational vertex operator algebra whose irreducible modules are exactly these admissible modules for $\hat{sl}_2$ and for which the fusion rules are calculated. It is also shown that the q-dimensions with respect to the new Virasoro algebra are modular functions.