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Fermionic solution of the Andrews-Baxter-Forrester model. II. Proof of Melzer's polynomial identities

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Abstract

We compute the one-dimensional configuration sums of the ABF model using the fermionic technique introduced in part I of this paper. Combined with the results of Andrews, Baxter, and Forrester, we prove polynomial identities for finitizations of the Virasoro characters\(\chi _{b.a}^{(r - 1.r)} (q)\) as conjectured by Melzer. In the thermodynamic limit these identities reproduce Rogers-Ramanujan-type identities for the unitary minimal Virasoro characters conjectured by the Stony Brook group. We also present a list of additional Virasoro character identities which follow from our proof of Melzer's identities and application of Bailey's lemma.

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  1. Mathematics Department, University of Melbourne, 3052, Parkville, Victoria, Australia

    S. Ole Warnaar

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Dedicated to the memory of Piet Kasteleyn.

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Warnaar, S.O. Fermionic solution of the Andrews-Baxter-Forrester model. II. Proof of Melzer's polynomial identities. J Stat Phys 84, 49–83 (1996). https://doi.org/10.1007/BF02179577

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