Metaplectic Whittaker functions and crystals of type B

Ben Brubaker, Daniel Bump, Gautam Chinta, Paul E. Gunnells

Research output: Chapter in Book/Report/Conference proceedingChapter

23 Scopus citations

Abstract

The spherical metaplectic Whittaker function on the double cover of Sp (2r, F), where F is a nonarchimedean local field, is considered from several different points of view. Previously, an expression, similar to the Casselman-Shalika formula, had been given by Bump, Friedberg, and Hoffstein as a sum is over the Weyl group. It is shown that this coincides with the expression for the p-parts of Weyl group multiple Dirichlet series of type Br as defined by the averaging method of Chinta and Gunnells. Two conjectural expressions as sums over crystals of type B are given and another as the partition function of a free-fermionic six-vertex model system.

Original languageEnglish (US)
Title of host publicationMultiple Dirichlet Series, L-functions and Automorphic Forms
PublisherBirkhauser Boston
Pages93-118
Number of pages26
ISBN (Electronic)9780817683344
ISBN (Print)9780817683337
DOIs
StatePublished - Jan 1 2012

Keywords

  • Chinta-gunnells averaging method
  • Crystal graph
  • Metaplectic whittaker function
  • Solvable lattice model
  • Weyl group multiple dirichlet series

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