Whittaker functions on metaplectic covers of GL(r)

Abstract

This paper establishes a combinatorial link between different approaches to constructing Whittaker functions on a metaplectic group over a non-archimedean local field. We prove a metaplectic analogue of Tokuyama's Theorem and give a crystal description of polynomials related to Iwahori-Whittaker functions. The proof relies on formulas of metaplectic Demazure and Demazure-Lusztig operators, proved previously in joint work with Gautam Chinta and Paul E. Gunnells.

50 pages, 8 figures

References in corpus (3)

• Metaplectic Demazure operators and Whittaker functions
• Weyl Group Multiple Dirichlet Series for Symmetrizable Kac-Moody Root Systems
• Unramified Whittaker Functions on p-adic Loop Groups

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• A Yang-Baxter equation for metaplectic ice
• Stochastic symplectic ice
• Metaplectic Iwahori Whittaker functions and supersymmetric lattice models
• Hecke Modules from Metaplectic Ice
• Relating three combinatorial formulas for type $A$ Whittaker functions