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We find higher rank generalizations of the Razumov--Stroganov sum rules at$q=-e^{i\pi\over k+1}$ for $A_{k-1}$ models with open boundaries, byconstructing polynomial solutions of level one boundary quantumKnizhnik--Zamolodchikov equations for $U_q(\frak{sl}(k))$. The result takes theform of a character of the symplectic group, that leads to a generalization ofthe number of vertically symmetric alternating sign matrices. We alsoinvestigate the other combinatorial point $q=-1$, presumably related to thegeometry of nilpotent matrix varieties.

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