## 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) |
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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 | |

State | Published - Jan 1 2012 |

## Keywords

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