Andrews-Gordon type identities from combinations of Virasoro characters

Boris Feigin, Omar Foda*, Trevor Welsh

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

For p ∈ {3,4} and all p′>p, with p′ coprime to p, we obtain fermionic expressions for the combination χ 1,s p,p′ +q Δ χ p-1,s p,p′ of Virasoro (W 2) characters for various values of s, and particular choices of Δ. Equating these expressions with known product expressions, we obtain q-series identities which are akin to the Andrews-Gordon identities. For p=3, these identities were conjectured by Bytsko. For p=4, we obtain identities whose form is a variation on that of the p=3 cases. These identities appear to be new. The case (p,p′)=(3,14) is particularly interesting because it relates not only to W 2, but also to W 3 characters, and offers W 3 analogues of the original Andrews-Gordon identities. Our fermionic expressions for these characters differ from those of Andrews et al. which involve Gaussian polynomials.

Original languageEnglish
Pages (from-to)33-52
Number of pages20
JournalRamanujan Journal
Volume17
Issue number1
DOIs
StatePublished - Oct 2008
Externally publishedYes

Keywords

  • Andrews-Gordon identities
  • q-series identities
  • Virasoro characters

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