Geodesic
Quantum Knizhnik–Zamolodchikov equation, totally symmetric
Teoretičeskaâ i matematičeskaâ fizika, Tome 154 (2008) no. 3, pp. 387-408 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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P. Zinn-Justin; Ph. Di Francesco. Quantum Knizhnik–Zamolodchikov equation, totally symmetric. Teoretičeskaâ i matematičeskaâ fizika, Tome 154 (2008) no. 3, pp. 387-408. http://geodesic.mathdoc.fr/item/TMF_2008_154_3_a0/

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