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Teoreticheskaya i Matematicheskaya Fizika, 2008, Volume 154, Number 3, Pages 387–408
DOI: https://doi.org/10.4213/tmf6178 (Mi tmf6178) 		 
This article is cited in 26 scientific papers (total in 26 papers)

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

P. Zinn-Justina, Ph. Di Francescob

a Laboratoire de Physique Théorique et Modèles Statistiques, Univ Paris-Sud, Orsay, France
b Service de Physique Théorique de Saclay, Gif sur Yvette Cedex, France
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DOI: https://doi.org/10.4213/tmf6178
Abstract: We present multiple-residue integral formulas for partial sums in the basis of link patterns of the polynomial solution of the level-$1$ $U_q(\widehat{\mathfrak{sl}_2})$ 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.
Keywords: loop model, combinatorics, quantum integrability.
English version:
Theoretical and Mathematical Physics, 2008, Volume 154, Issue 3, Pages 331–348
DOI: https://doi.org/10.1007/s11232-008-0031-x
Bibliographic databases:
Language: Russian
Citation: P. Zinn-Justin, Ph. Di Francesco, “Quantum Knizhnik–Zamolodchikov equation, totally symmetric self-complementary plane partitions, and alternating sign matrices”, TMF, 154:3 (2008), 387–408; Theoret. and Math. Phys., 154:3 (2008), 331–348
Citation in format AMSBIB
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    • This publication is cited in the following 26 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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