Boundary qKZ equation and generalized Razumov-Stroganov sum rules for open IRF models

We find higher-rank generalizations of the Razumov-Stroganov sum rules at q = -e(i pi/(k+1)) for A(k-1) models with open boundaries, by constructing polynomial solutions of level-1 boundary quantum Knizhnik-Zamolodchikov equations for U-q(sl(k)). The result takes the form of a character of the symplectic group, that leads to a generalization of the number of vertically symmetric alternating sign matrices. We also investigate the other combinatorial point q = -1, presumably related to the geometry of nilpotent matrix varieties.