Authors: Dražen Adamović, Victor G. Kac, Pierluigi Möseneder Frajria, Paolo Papi, Ozren Perše

Selecta Mathematica, pp 1–44

https://doi.org/10.1007/s00029-017-0386-7

Abstract: We complete the classification of conformal embeddings of a maximally reductive subalgebra a simple Lie algebra at non-integrable non-critical levels *k* by dealing with the case when has rank less than that of . We describe some remarkable instances of decomposition of the vertex algebra \mathfrak{k} as a module for the vertex subalgebra generated by . 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 at level , and obtain explicit branching rules by applying certain *q*-series identity. In the analysis of conformal embedding at level we detect subsingular vectors which do not appear in the branching rules of the classical Howe dual pairs.

Keywords: Conformal embedding Vertex operator algebra Non-equal rank subalgebra Howe dual pairs q-series identity

Mathematics Subject Classification: Primary 17B69, Secondary 17B20 17B65