Peter J. McNamara

Metaplectic whittaker functions and crystal bases

We study Whittaker functions on nonlinear coverings of simple algebraic groups over a nonarchimedean 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 prime-power-supported coefficients of multiple Dirichlet series.

Principal Series Representations of Metaplectic Groups Over Local Fields

Let G be a split reductive algebraic group over a non-archimedean local field. We study the representation theory of a central extension \(\widetilde{G}\) of G by a cyclic group of order n, under some mild tameness assumptions on n. In particular, we focus our attention on the development of the theory of principal series representations for \(\widetilde{G}\) and its applications to the study of Hecke algebras via a Satake isomorphism.