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

2007/03/03 by P. Di Francesco, Di Francesco, P., P. Zinn-Justin +1
Mathematics · Physics and Astronomy · #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.CO #math.MP

paper · pdf · doi:10.48550/arxiv.math-ph/0703015

arxiv created 2007/04/20 · arxiv updated 2009/12/01

Abstract

We present multiresidue formulae for partial sums in the basis of link patterns of the polynomial solution to the level 1 U_q( sl₂) 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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