Andrews-Gordon identities from combinations of Virasoro characters

Abstract

For p \in {3, 4} and all p' > p, with p' coprime to p, we obtain fermionic expressions for the combination χ^{p, p'}_{1, s} + q^Δ χ^{p, p'}_{p-1,s} of Virasoro (W_2) characters for various values of s, and particular choices of Delta. 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.

arXiv comment18 pages, latex. Improved exposition, added comments for clarity, added references. No changes to content. The Ramanujan Journal, published online on September 21, 2007 via http://www.springerlink.com/content/478544t414l26v05/

References in corpus (8)

• Fermionic Sum Representations for Conformal Field Theory Characters
• Rogers-Schur-Ramanujan type identities for the $M(p,p^{\prime })$ minimal models of conformal field theory
• Continued Fractions and Fermionic Representations for Characters of M(p,p') minimal models
• Virasoro character identities from the Andrews--Bailey construction
• Fermionic expressions for minimal model Virasoro characters
• Fermionic representations for characters of M(3,t), M(4,5), M(5,6) and M(6,7) minimal models and related Rogers-Ramanujan type and dilogarithm identities
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Cited by in corpus (11)

• A framework of Rogers-Ramanujan identities and their arithmetic properties
• A quasi-particle description of the M(3,p) models
• Coupling of two conformal field theories and Nakajima-Yoshioka blow-up equations
• Cylindric partitions, W_r characters and the Andrews-Gordon-Bressoud identities
• BPS Indices, Modularity and Perturbations in Quantum K-theory
• Closed form fermionic expressions for the Macdonald index
• Embedding of bases: from the M(2,2k+1) to the M(3,4k+2-delta) models
• The ${\mathrm{A}}_2$ Andrews-Gordon identities and cylindric partitions
• The A_{2n}^{(2)} Rogers-Ramanujan identities
• Factorization of alternating sums of Virasoro characters
• Virasoro representations with central charges $\frac{1}{2}$ and 1 on the real neutral fermion Fock space $F^{\otimes \frac{1}{2}}$