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 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-1(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. (C) 2008 Elsevier Inc. All rights reserved.