Abstract
We find higher-rank generalizations of the Razumov-Stroganov sum rules at q ≤ -ei π/(k+1) for Ak-1 models with open boundaries, by constructing polynomial solutions of level-1 boundary quantum Knizhnik-Zamolodchikov equations for . 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.
Original language | English (US) |
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Pages (from-to) | 57-74 |
Number of pages | 18 |
Journal | Journal of Statistical Mechanics: Theory and Experiment |
Issue number | 11 |
DOIs | |
State | Published - Nov 1 2005 |
Externally published | Yes |
Keywords
- Algebraic structures of integrable models
- Integrable spin chains (vertex models)
- Loop models and polymers
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Statistics, Probability and Uncertainty