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In his famous ASM paper, Kuperberg uses a skein relation to give an algebraicproof of a Yang-Baxter equation where the Boltzmann weights satisfy thefield-free condition. In this paper, we use Kuperberg's techniques to giveproofs of a few Yang-Baxter equations where the Boltzmann weights satisfy thefree-fermionic condition. In particular, we use skein relations to prove theYang-Baxter equation for Gamma-Gamma ice which is a free-fermionic six-vertexmodel introduced by Brubaker, Bump and Friedberg.

Free-fermionic ice, the Yang-Baxter equation and skein relations