Using the theory of intertwining operators for vertex operator algebras we show that the graded dimensions of the principal subspaces associated to the standard modules for [InlineMediaObject not available: see fulltext.] satisfy certain classical recursion formulas of Rogers and Selberg. These recursions were exploited by Andrews in connection with Gordon's generalization of the Rogers-Ramanujan identities and with Andrews' related identities. The present work generalizes the authors' previous work on intertwining operators and the Rogers-Ramanujan recursion.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Affine Lie algebras
- Difference equations
- Vertex operator algebras