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

1995/08/17 by S. Ole Warnaar, S. O. Warnaar · 5 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #hep-th

paper · pdf · doi:10.1007/bf02179577

28 pages, Latex, 7 Postscript figures

arxiv created 1995/08/17 · openalex publication_date 1996/07/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

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 find proof of polynomial identities for finitizations of the Virasoro characters χ_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.

Citations

• Supersymmetric Analogs of the Gordon-Andrews Identities, and Related TBA Systems

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