Quantum Knizhnik-Zamolodchikov equation: reflecting boundary conditions and combinatorics
P. Di Francesco, P. Zinn-Justin
TL;DR
This paper solves the quantum Knizhnik-Zamolodchikov equation with reflecting boundaries, linking it to combinatorial enumeration problems and proving related conjectures using integral formulas.
Contribution
It introduces integral formulae for solutions and establishes a connection between quantum algebra and combinatorics, specifically cyclically symmetric plane partitions.
Findings
Proved conjectures relating QKZ solutions to combinatorial enumeration.
Derived integral formulae for the level 1 QKZ solutions with reflecting boundaries.
Connected quantum algebra solutions to combinatorial objects like plane partitions.
Abstract
We consider the level 1 solution of quantum Knizhnik-Zamolodchikov equation with reflecting boundary conditions which is relevant to the Temperley--Lieb model of loops on a strip. By use of integral formulae we prove conjectures relating it to the weighted enumeration of Cyclically Symmetric Transpose Complement Plane Partitions and related combinatorial objects.
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