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 $A_{\ell }^{(1)}$. These vertex operator algebras are constructed by using the explicit construction of certain singular vectors in the universal affine vertex operator algebra $N(n-2,0)$ 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 $\mathcal{O}$. In the case $l=2$, we show that the vertex operator algebra $N(n-2,0)$ contains two linearly independent singular vectors of the same conformal weight.

15 pages, LaTeX; final version, to appear in J. Algebra

References in corpus (3)

• Vertex Algebras and Algebraic Curves
• Annihilating fields of standard modules of sl(2,C)~ and combinatorial identities
• Some Rational Vertex Algebras

Cited by in corpus (7)

• Tensor categories of affine Lie algebras beyond admissible levels
• Fusion rules and complete reducibility of certain modules for affine Lie algebras
• An application of collapsing levels to the representation theory of affine vertex algebras
• The Vertex Algebra $M(1{)}^{+}$ and Certain Affine Vertex Algebras of Level -1
• On the representation theory of the vertex algebra $L_{-5/2}(sl(4))$
• Simple modules for Affine vertex algebras in the minimal nilpotent orbit
• Associated varieties of simple affine VOAs $L_k(s{l}_3)$ and $W$-algebras $W_k(s{l}_3,f)$