Metaplectic Whittaker Functions and Crystal Bases

Abstract

We study Whittaker functions on nonlinear coverings of simple algebraic groups over a non-archimedean local field. We produce a recipe for expressing such a Whittaker function as a weighted sum over a crystal graph, and show that in type A, these expressions agree with known formulae for the prime power supported coefficients of Multiple Dirichlet Series.

26 pages, version to appear

References in corpus (1)

• Principal series representations of metaplectic groups over local fields

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• Principal series representations of metaplectic groups over local fields
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• Weyl Group Multiple Dirichlet Series for Symmetrizable Kac-Moody Root Systems
• Yang-Baxter Equations for General Metaplectic Ice
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• On the crystal graph description of the stable Weyl group multiple Dirichlet series
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• Relating three combinatorial formulas for type $A$ Whittaker functions