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Quantum Knizhnik-Zamolodchikov Equation, Totally Symmetric Self-Complementary Plane Partitions and Alternating Sign Matrices

P. Di Francesco·P. Zinn-Justin
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Abstract

We present multiresidue formulae for partial sums in the basis of link patterns of the polynomial solution to the level 1 U_q(\hat sl_2) quantum Knizhnik--Zamolodchikov equation at generic values of the quantum parameter q. These allow for rewriting and generalizing a recent conjecture [Di Francesco '06] connecting the above 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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P. Di Francesco, P. Zinn-Justin. 2007-04-20. Quantum Knizhnik-Zamolodchikov Equation, Totally Symmetric Self-Complementary Plane Partitions and Alternating Sign Matrices. https://arxiv.org/abs/math-ph/0703015

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