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Andrews-Gordon identities from combinations of Virasoro characters

Boris Feigin·Omar Foda·Trevor Welsh
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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.

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Boris Feigin, Omar Foda, Trevor Welsh. 2006-02-14. Andrews-Gordon identities from combinations of Virasoro characters. https://doi.org/10.1007/s11139-006-9011-7

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