The Rogers-Selberg recursions, the Gordon-Andrews identities and intertwining operators

S. Capparelli, J. Lepowsky, A. Milas

Research output: Contribution to journalArticlepeer-review

42 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)379-397
Number of pages19
JournalRamanujan Journal
Issue number3
StatePublished - Dec 2006

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory


  • Affine Lie algebras
  • Difference equations
  • Vertex operator algebras


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