Metaplectic Whittaker functions and crystals of type B

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

doi:10.1007/978-0-8176-8334-4_4

Metaplectic Whittaker functions and crystals of type B

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

School of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

15 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 B_r 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 language	English (US)
Title of host publication	Multiple Dirichlet Series, L-functions and Automorphic Forms
Publisher	Birkhauser Boston
Pages	93-118
Number of pages	26
ISBN (Electronic)	9780817683344
ISBN (Print)	9780817683337
DOIs	https://doi.org/10.1007/978-0-8176-8334-4_4
State	Published - 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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10.1007/978-0-8176-8334-4_4

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AU - Bump, Daniel

AU - Chinta, Gautam

AU - Gunnells, Paul E.

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N2 - 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.

AB - 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.

KW - Chinta-gunnells averaging method

KW - Crystal graph

KW - Metaplectic whittaker function

KW - Solvable lattice model

KW - Weyl group multiple dirichlet series

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Metaplectic Whittaker functions and crystals of type B

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