The~symmetry of the~partition function of some square ice models
Teoretičeskaâ i matematičeskaâ fizika, Tome 161 (2009) no. 3, pp. 309-317
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We consider the partition function $Z(N;x_1,\dots,x_N,y_1,\dots,y_N)$ of the square ice model with domain wall boundary conditions. We give a simple proof that $Z$ is symmetric with respect to all its variables when the global parameter $a$ of the model is set to the special value $a=e^{i\pi/3}$. Our proof does not use any determinant interpretation of $Z$ and can be adapted to other situations (e.g., to some symmetric ice models).
Keywords:
alternating-sign matrix, square ice model, partition function, Yang–Baxter equation.
@article{TMF_2009_161_3_a0,
author = {J.-Ch. Aval},
title = {The~symmetry of the~partition function of some square ice models},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {309--317},
publisher = {mathdoc},
volume = {161},
number = {3},
year = {2009},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2009_161_3_a0/}
}
J.-Ch. Aval. The~symmetry of the~partition function of some square ice models. Teoretičeskaâ i matematičeskaâ fizika, Tome 161 (2009) no. 3, pp. 309-317. http://geodesic.mathdoc.fr/item/TMF_2009_161_3_a0/