SPECTRAL TRANSFER FOR METAPLECTIC GROUPS. I. LOCAL CHARACTER RELATIONS

Local Coefficient Matrices of Metaplectic Groups

The principal series representations of the n-fold metaplectic covers of the general linear group GLr(F) were described in the foundational paper “Metaplectic Forms,” by Kazhdan and Patterson (1984). In this paper, we study the local coefficient matrices for a certain class of principal series representations over GL2(F), where F is a nonarchimedean local field. The local coefficient matrices c...

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 G̃ 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 G̃ and its applications to the study of Hecke algebras via a Satake is...

Automorphic Forms and Metaplectic Groups

In 1952, Gelfand and Fomin noticed that classical modular forms were related to representations of SL2(R). As a result of this realization, Gelfand later defined GLr automorphic forms via representation theory. A metaplectic form is just an automorphic form defined on a cover of GLr, called a metaplectic group. In this talk, we will carefully construct the metaplectic covers of GL2(F) where F i...

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...

Twisted Whittaker models for metaplectic groups