Descent and theta functions for metaplectic groups

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...

Theta functions on covers of symplectic groups

We study the automorphic theta representation $Theta_{2n}^{(r)}$ on the $r$-fold cover of the symplectic group $Sp_{2n}$‎. ‎This representation is obtained from the residues of Eisenstein series on this group‎. ‎If $r$ is odd‎, ‎$nle r

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...

Twisted Whittaker models for metaplectic groups

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...