Loop model with mixed boundary conditions, qKZ equation and alternating sign matrices
Mathematical Physics
2009-11-11 v2 Combinatorics
math.MP
Abstract
The integrable loop model with mixed boundary conditions based on the 1-boundary extended Temperley--Lieb algebra with loop weight 1 is considered. The corresponding qKZ equation is introduced and its minimal degree solution described. As a result, the sum of the properly normalized components of the ground state in size L is computed and shown to be equal to the number of Horizontally and Vertically Symmetric Alternating Sign Matrices of size 2L+3. A refined counting is also considered.
Cite
@article{arxiv.math-ph/0610067,
title = {Loop model with mixed boundary conditions, qKZ equation and alternating sign matrices},
author = {P. Zinn-Justin},
journal= {arXiv preprint arXiv:math-ph/0610067},
year = {2009}
}