The Ramanujan Journal

, Volume 17, Issue 1, pp 33–52 | Cite as

Andrews–Gordon type identities from combinations of Virasoro characters



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.


Andrews–Gordon identities q-Series identities Virasoro characters 

Mathematics Subject Classification (2000)

05A30 05A19 17B68 81T40 11P82 


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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Landau Institute for Theoretical PhysicsMoscow regionRussia
  2. 2.Department of Mathematics and StatisticsUniversity of MelbourneVictoriaAustralia
  3. 3.School of MathematicsUniversity of SouthamptonSouthamptonUK

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