The structure of Verma modules over the \(N=2\) superconformal algebra (Q1296253)

The \(N=2\) superconformal algebra \(\mathcal{A}\) (or, the \(N=2\) supersymmetric extension of the Virasoro algebra) does not have a canonical triangular decomposition. Thus, the authors define two different types of Verma-like modules over \(\mathcal{A}\), called topological Verma modules and massive Verma modules, and study their submodule structure. The main result of the paper is the explicit formulae for singular vectors in any Verma module, which, in particular, describes all embeddings between them. Additionally a general formulae for subsingular vectors are also obtained. This allows the authors to describe the structure of submodules in \(N=2\) Verma modules. In particular, the embedding diagrams for topological Verma modules are proved to be isomorphic to those of \(\widehat{sl(2)}\) Verma modules.