Representations of certain non-rational vertex operator algebras of affine type

Abstract

In this paper we study a series of vertex operator algebras of integer level associated to the affine Lie algebra A ℓ ( 1 ) . These vertex operator algebras are constructed by using the explicit construction of certain singular vectors in the universal affine vertex operator algebra N l ( n − 2 , 0 ) at the integer level. In the case n = 1 or l = 2 , we explicitly determine Zhu's algebras and classify all irreducible modules in the category O . In the case l = 2 , we show that the vertex operator algebra N 2 ( n − 2 , 0 ) contains two linearly independent singular vectors of the same conformal weight.