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

In this paper we study a series of vertex operator algebras of integer level associated to the affine Lie algebra . These vertex operator algebras are constructed by using the explicit construction of certain singular vectors in the universal affine vertex operator algebra Nl(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 N2(n−2,0) contains two linearly independent singular vectors of the same conformal weight.