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

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

2005-09-06

arxiv.org/abs/math-ph/0509011v3

Physics

Mathematical Physics

21 pages, 7 figures, 1 table, uses epsf and lanlmac conclusion slightly modified

Scientific paper

10.1088/1742-5468/2005/11/P11003

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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