Metaplectic Whittaker functions and crystal bases

Metaplectic Whittaker Functions and Crystal Bases

We study Whittaker functions on nonlinear coverings of simple algebraic groups over a non-archimedean local field. We produce a recipe for expressing such a Whittaker function as a weighted sum over a crystal graph, and show that in type A, these expressions agree with known formulae for the p-part of Multiple Dirichlet Series.

Whittaker Functions on Metaplectic Groups

The theory of Whittaker functions is of crucial importance in the classical study of automorphic forms on adele groups. Motivated by the appearance of Whittaker functions for covers of reductive groups in the theory of multiple Dirichlet series, we provide a study of Whittaker functions on metaplectic covers of reductive groups over local fields. Thesis Supervisor: Benjamin Brubaker Title: Assi...

Metaplectic Whittaker Functions and Crystals of Type B

Let n be an integer and let F be a nonarchimedean local field whose characteristic is not a prime dividing n. Let μk be the group of k-th roots of unity in the algebraic closure of F ; we assume that μ2n ⊂ F . Let G be a split, simply-connected semisimple algebraic group over F . We assume that G is actually defined over the ring o of integers in F in such a way that K = G(o) is a special maxim...

Whittaker Coefficients of Metaplectic Eisenstein Series

We study Whittaker coefficients for maximal parabolic Eisenstein series on metaplectic covers of split reductive groups. By the theory of Eisenstein series these coefficients have meromorphic continuation and functional equation. However they are not Eulerian and the standard methods to compute them in the reductive case do not apply to covers. For “cominuscule” maximal parabolics, we give an e...

Twisted Whittaker models for metaplectic groups