Metaplectic Ice
Ben Brubaker, Daniel Bump, Gautam Chinta, Solomon Friedberg, Paul, E. Gunnells

TL;DR
This paper explores the connection between metaplectic Whittaker functions on certain algebraic groups and statistical mechanical models, revealing new algebraic and combinatorial insights into their properties.
Contribution
It demonstrates that properties of metaplectic Whittaker functions can be expressed via transfer matrices and suggests proof methods using the Yang-Baxter equation.
Findings
Whittaker functions relate to six-vertex model variants
Properties can be expressed through transfer matrix commutativity
Potential proof strategies involve the Yang-Baxter equation
Abstract
Spherical Whittaker functions on the metaplectic n-fold cover of GL(r+1) over a nonarchimedean local field containing n distinct n-th roots of unity may be expressed as the partition functions of statistical mechanical systems that are variants of the six-vertex model. If n=1 then in view of the Casselman-Shalika formula this fact is related to Tokuyama's deformation of the Weyl character formula. It is shown that various properties of these Whittaker functions may be expressed in terms of the commutativity of row transfer matrices for the system. Potentially these properties (which are already proved by other methods, but very nontrivial) are amenable to proof by the Yang-Baxter equation.
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Taxonomy
TopicsCancer, Hypoxia, and Metabolism · Adrenal Hormones and Disorders
