A new left-moving family of colored lattice models is proven solvable and dual to the right-moving family, with the crystal limit yielding a Schützenberger involution bijection on Gelfand-Tsetlin patterns.
Duality for metaplectic ice
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abstract
We interpret values of spherical Whittaker functions on metaplectic covers of the general linear group over a nonarchimedean local field as partition functions of two different solvable lattice models. We prove the equality of these two partition functions by showing the commutativity of transfer matrices associated to different models via the Yang-Baxter equation.
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The Sch\"utzenberger involution and colored lattice models
A new left-moving family of colored lattice models is proven solvable and dual to the right-moving family, with the crystal limit yielding a Schützenberger involution bijection on Gelfand-Tsetlin patterns.