Andrews-Gordon identities from combinations of Virasoro characters

Details Andrews-Gordon identities from combinations of Virasoro characters Andrews-Gordon identities from combinations of Virasoro characters

2005-04-05

arxiv.org/abs/math-ph/0504014v3

RamanujanJ.17:33-52,2008

Physics

Mathematical Physics

18 pages, latex. Improved exposition, added comments for clarity, added references. No changes to content. The Ramanujan Journ

Scientific paper

10.1007/s11139-006-9011-7

For p \in {3, 4} and all p' > p, with p' coprime to p, we obtain fermionic expressions for the combination \chi^{p, p'}_{1, s} + q^{\Delta} \chi^{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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