On the symmetry of the partition function of some square ice models

Details On the symmetry of the partition function of some square ice models On the symmetry of the partition function of some square ice models

2009-03-04

arxiv.org/abs/0903.0777v1

Theoretical and Mathematical Physics 161, 3 (2009) 1582-1589

Mathematics

Combinatorics

8 pages

Scientific paper

We consider the partition function Z(N;x_1,...,x_N,y_1,...,y_N) of the square ice model with domain wall boundary. We give a simple proof of the symmetry of Z with respect to all its variables when the global parameter a of the model is set to the special value a=exp(i\pi/3). Our proof does not use any determinantal interpretation of Z and can be adapted to other situations (for examples to some symmetric ice models).

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