Metaplectic theta functions and global integrals

Theta Hypergeometric Integrals

A general class of (multiple) hypergeometric type integrals associated with the Jacobi theta functions is defined. These integrals are related to theta hypergeometric series via the residue calculus. In the one variable case, theta function extensions of the Meijer function are obtained. A number of multiple generalizations of the elliptic beta integral associated with the root systems An and C...

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...

Moduli of metaplectic bundles on curves and Theta-sheaves

Historically θ-series have been one of the major methods of constructing automorphic forms. A representation-theoretic appoach to the theory of θ-series, as discoved by A. Weil [18] and extended by R. Howe [12], is based on the oscillator representation of the metaplectic group (cf. [17] for a recent survey). In this paper we propose a geometric interpretation this representation (in the nonram...

Feynman path integrals on phase space and the metaplectic representation

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.