On some ground state components of the O(1) loop model

T. Fonseca (1) , Paul Zinn-Justin (1)

1 LPTHE - Laboratoire de Physique Théorique et Hautes Energies

We address a number of conjectures about the ground state O(1) loop model, computing in particular two infinite series of partial sums of its entries and relating them to the enumeration of plane partitions. Our main tool is the use of integral formulae for a polynomial solution of the quantum Knizhnik-Zamolodchikov equation.

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Combinatoire [math.CO]; Mécanique statistique [cond-mat.stat-mech]

T. Fonseca, Paul Zinn-Justin. On some ground state components of the O(1) loop model. Journal of Statistical Mechanics: Theory and Experiment, 2009, pp.P03025. ⟨hal-00399254⟩