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

Abstract

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
Volume12
Issue number3
DOIs
StatePublished - Dec 2006

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Keywords

  • Affine Lie algebras
  • Difference equations
  • Vertex operator algebras

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