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

Stefano Capparelli·James Lepowsky·Antun Milas
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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 $\hat{\goth{sl}(2)}$ 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.

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Stefano Capparelli, James Lepowsky, Antun Milas. 2006-12-10. The Rogers-Selberg recursions, the Gordon-Andrews identities and intertwining operators. https://arxiv.org/abs/math/0310080

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