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

for Ak−1 models with open boundaries, by constructing polynomial solutions of level one boundary quantum Knizhnik–Zamolodchikov equations for Uq(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.