Metaplectic Ice
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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].
Date issued
2012Department
Massachusetts Institute of Technology. Department of MathematicsJournal
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
ISBN
978-0-8176-8333-7
978-0-8176-8334-4