Quantum Knizhnik-Zamolodchikov equation: reflecting boundary conditions and combinatorics

P. Di Francesco (1) , Paul Zinn-Justin (2)

1 SPhT - Service de Physique Théorique
2 LPTHE - Laboratoire de Physique Théorique et Hautes Energies

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.

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Combinatoire [math.CO]; Systèmes Solubles et Intégrables [nlin.SI]

P. Di Francesco, Paul Zinn-Justin. Quantum Knizhnik-Zamolodchikov equation: reflecting boundary conditions and combinatorics. Journal of Statistical Mechanics: Theory and Experiment, 2007, pp.P12009. ⟨hal-00203605⟩