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Quantum Knizhnik-Zamolodchikov equation, totally symmetric self-complementary plane partitions, and alternating sign matrices

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Abstract

We present multiple-residue integral formulas for partial sums in the basis of link patterns of the polynomial solution of the level-1 \(U_q (\widehat{\mathfrak{s}\mathfrak{l}_2 })\) quantum Knizhnik-Zamolodchikov equation at arbitrary values of the quantum parameter q. These formulas allow rewriting and generalizing a recent conjecture of Di Francesco connecting these sums to generating polynomials for weighted totally symmetric self-complementary plane partitions. We reduce the corresponding conjectures to a single integral identity, yet to be proved.

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Authors and Affiliations

  1. Laboratoire de Physique Théorique et Modèles Statistiques, Univ Paris-Sud, Orsay, France

    P. Zinn-Justin

  2. Service de Physique Théorique de Saclay, Gif sur Yvette Cedex, France

    P. Di Francesco

Authors
  1. P. Zinn-Justin
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  2. P. Di Francesco
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Correspondence to P. Zinn-Justin.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 3, pp. 387–408, March, 2008.

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Zinn-Justin, P., Di Francesco, P. Quantum Knizhnik-Zamolodchikov equation, totally symmetric self-complementary plane partitions, and alternating sign matrices. Theor Math Phys 154, 331–348 (2008). https://doi.org/10.1007/s11232-008-0031-x

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  • DOI: https://doi.org/10.1007/s11232-008-0031-x

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