Vertex operator algebras and representations of affine Lie algebras (Q1815379)

This paper summarizes work of the authors in a preprint entitled ``Annihilating fields of standard modules of \({\mathfrak sl} (2,\mathbb{C})\) and combinatorial identities.'' The authors announce the construction of an explicit basis for all integrable highest weight modules over the Lie algebra \(A_1^{(1)}\). The construction uses representations of vertex operator algebras and leads to combinatorial identities of Rogers-Ramanujan type.