Refined Razumov-Stroganov conjectures for open boundaries

Abstract

Recently it has been conjectured that the ground state of a Markovian Hamiltonian, with one boundary operator, acting in a link pattern space is related to vertically and horizontally symmetric alternating-sign matrices (equivalently fully packed loop configurations (FPL) on a grid with special boundaries). We extend this conjecture by introducing an arbitrary boundary parameter. We show that the parameter dependent ground state is related to refined vertically symmetric alternating-sign matrices, i.e. with prescribed configurations (respectively, prescribed FPL configurations) in the next to central row. We also conjecture a relation between the ground state of a Markovian Hamiltonian with ..