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Metaplectic Whittaker Functions and Crystals of Type B

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Multiple Dirichlet Series, L-functions and Automorphic Forms

Part of the book series: Progress in Mathematics ((PM,volume 300))

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.

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Author information

Authors and Affiliations

  1. Department of Mathematics, MIT, Cambridge, MA, 02139–4307, USA

    Ben Brubaker

  2. Department of Mathematics, Stanford University, Stanford, CA, 94305–2125, USA

    Daniel Bump

  3. Department of Mathematics, The City College of New York, New York, NY, 10031, USA

    Gautam Chinta

  4. Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA, 01003, USA

    Paul E. Gunnells

Authors
  1. Ben Brubaker
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  2. Daniel Bump
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  3. Gautam Chinta
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  4. Paul E. Gunnells
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Corresponding author

Correspondence to Daniel Bump .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Stanford University, Stanford, 94305-2125, California, USA

    Daniel Bump

  2. , Department of Mathematics, Boston College, Commonwealth Ave. 140, Chestnut Hill, 02467-3806, Massachusetts, USA

    Solomon Friedberg

  3. , Department of Mathematics, Columbia University, Broadway 2990, New York, 10027, New York, USA

    Dorian Goldfeld

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Brubaker, B., Bump, D., Chinta, G., Gunnells, P.E. (2012). Metaplectic Whittaker Functions and Crystals of Type B. In: Bump, D., Friedberg, S., Goldfeld, D. (eds) Multiple Dirichlet Series, L-functions and Automorphic Forms. Progress in Mathematics, vol 300. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8334-4_4

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