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

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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 languageEnglish (US)
Pages (from-to)57-74
Number of pages18
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue number11
DOIs
StatePublished - Nov 1 2005
Externally publishedYes

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

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