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

Abstract

We address a number of conjectures concerning 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. © 2009 IOP Publishing Ltd. and SISSA.