Boundary qKZ equation and generalized Razumov-Stroganov sum rules for open IRF models
Résumé
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, by constructing polynomial solutions of level one boundary quantum Knizhnik--Zamolodchikov equations for $U_q(\frak{sl}(k))$. 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.
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