Fermionic solution of the Andrews-Baxter-Forrester model II: proof of Melzer's polynomial identities

Details Fermionic solution of the Andrews-Baxter-Forrester model II: proof of Melzer's polynomial identities Fermionic solution of the Andrews-Baxter-Forrester model II: proof of Melzer's polynomial identities

1995-08-17

arxiv.org/abs/hep-th/9508079v2

Physics

High Energy Physics

High Energy Physics - Theory

28 pages, Latex, 7 Postscript figures

Scientific paper

10.1007/BF02179577

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 find proof of 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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