Boundary qKZ equation and generalized Razumov-Stroganov sum rules for open IRF models
Di Francesco, P.
arXiv, 0509011 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2005-09-06
Classification:  Mathematical Physics,  Condensed Matter - Statistical Mechanics,  Mathematics - Combinatorics 
@article{0509011,
     author = {Di Francesco, P.},
     title = {Boundary qKZ equation and generalized Razumov-Stroganov sum rules for
  open IRF models},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0509011}
}

Di Francesco, P. Boundary qKZ equation and generalized Razumov-Stroganov sum rules for
  open IRF models. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0509011/