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

被引:9
|
作者
Di Francesco, P [1 ]
机构
[1] CEA, DSM,SPhT, CNRS,UMR 2306, Serv Phys Theor Saclay, F-91191 Gif Sur Yvette, France
关键词
algebraic structures of integrable models; integrable spin chains (vertex models); loop models and polymers;
D O I
10.1088/1742-5468/2005/11/P11003
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
We find higher-rank generalizations of the Razumov-Stroganov sum rules at q = -e(i pi/(k+1)) for A(k-1) models with open boundaries, by constructing polynomial solutions of level-1 boundary quantum Knizhnik-Zamolodchikov equations for U-q(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.
引用
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页码:57 / 74
页数:18
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