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Weyl Group Multiple Dirichlet Series by Ben Brubaker, Daniel Bump, Solomon Friedberg

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Chapter Nineteen

Statement B and the Yang-Baxter Equation

The p-parts of Weyl group multiple Dirichlet series, with their deformed Weyl denominators, may be expressed as partition functions of exactly solved models in statistical mechanics. The transition to ice-type models represents a subtle shift in emphasis from the crystal basis representation, and suggests the introduction of a new tool, the Yang-Baxter equation. This tool was introduced by Baxter [1] for proving the commutativity of row transfer matrices for the six-vertex and similar models. This is significant for us, because Statement B can be formulated in terms of the commutativity of two row transfer matrices. This last reformulation opens the door to a wide array of possible connections ...

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