Quantum Knizhnik-Zamolodchikov Equation, Totally Symmetric Self-Complementary Plane Partitions and Alternating Sign Matrices
Mathematical Physics
2007-05-23 v2 Combinatorics
math.MP
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.
Keywords
Cite
@article{arxiv.math-ph/0703015,
title = {Quantum Knizhnik-Zamolodchikov Equation, Totally Symmetric Self-Complementary Plane Partitions and Alternating Sign Matrices},
author = {P. Di Francesco and P. Zinn-Justin},
journal= {arXiv preprint arXiv:math-ph/0703015},
year = {2007}
}