Metaplectic Ice
Name
Brubaker_Metaplectic Ice.pdf
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379.95 KB
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9ff9b6d09ced4a2dd6d1ebeff4a294f7
Date Issued
2012
Journal
Progress in Mathematics
Publisher
Birkhauser Boston
Citation
Brubaker, Ben et al. “Metaplectic Ice.” Multiple Dirichlet Series, L-functions and Automorphic Forms. Ed. Daniel Bump, Solomon Friedberg, & Dorian Goldfeld. Boston, MA: Birkhäuser Boston, Progress in Mathematics 300 (2012): 65–92.
Version
Author's final manuscript
Abstract
We study spherical Whittaker functions on a metaplectic cover of
GL(r + 1) over a nonarchimedean local eld using lattice models from statistical
mechanics. An explicit description of this Whittaker function was given in terms
of Gelfand-Tsetlin patterns in [5, 17], and we translate this description into an
expression of the values of the Whittaker function as partition functions of a six-
vertex model. Properties of the Whittaker function may then be expressed in terms
of the commutativity of row transfer matrices potentially amenable to proof using
the Yang-Baxter equation. We give two examples of this: rst, the equivalence of
two di erent Gelfand-Tsetlin de nitions, and second, the e ect of the Weyl group
action on the Langlands parameters. The second example is closely connected
with another construction of the metaplectic Whittaker function by averaging over
a Weyl group action [9, 10].
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
http://dx.doi.org/10.1007/978-0-8176-8334-4_3
https://doi.org/10.1007/978-0-8176-8334-4_3
