Resumen de On the classification of non-equal rank affine conformal embeddings and applications
Drazen Adamovic, Victor G. Kac, Pierluigi Möseneder Frajria, Paolo Papi, Ozren Perse
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.
