Finiteness and orbifold Vertex Operator Algebras

In this paper, I investigate the ascending chain condition of right ideals in the case of vertex operator algebras satisfying a finiteness and/or a simplicity condition. Possible applications to the study of finiteness of orbifold VOAs is discussed.Comment: 12 pages, comments are welcom

On the classification of non-equal rank affine conformal embeddings and applications

We complete the classification of conformal embeddings of a maximally reductive subalgebra k into a simple Lie algebra g at non-integrable non-critical levels k by dealing with the case when k has rank less than that of g. We describe some remarkable instances of decomposition of the vertex algebra Vk (g) as a module for the vertex subalgebra generated by k. We discuss decompositions of conformal embeddings and constructions of new affine Howe dual pairs at negative levels. In particular, we study an example of conformal embeddings A1 × A1 → C3 at level k = −1/2, and obtain explicit branching rules by applying certain q-series identity. In the analysis of conformal embedding A1 × D4 → C8 at level k = −1/2 we detect subsingular vectors which do not appear in the branching rules of the classical Howe dual pairs