Unramified Whittaker functions for certain Brylinski–Deligne covering 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...

On Certain Groups of Functions

Let C(X,G) denote the group of continuous functions from a topological space X into a topological group G with the pointwise multiplication and the compact-open topology. We show that there is a natural topology on the collection of normal subgroups A(X) of C(X,G) of the M {f C(X,G): f(p) e} which is P analogous to the hull-kernel topology on the commutative Banach algegra C(X) of all continuou...

Whittaker Functions on Quantum Groups and Q-deformed Toda Operators

Let G be a simply connected simple Lie group over C. Let N± be the positive and the negative maximal unipotent subgroups, and H the maximal torus, corresponding to some polarization of G. Let G0 = N−HN+ be the big Bruhat cell. Let χ± : N± → C be holomorphic nondegenerate characters (i.e. they don’t vanish on simple roots). A Whittaker function on G0 with characters χ+, χ− is any holomorphic fun...

Whittaker Supports for Representations of Reductive Groups

Let F be either R or a finite extension of Qp, and let G be a finite central extension of the group of F -points of a reductive group defined over F . Also let π be a smooth representation of G (Fréchet of moderate growth if F = R). For each nilpotent orbit O we consider a certain Whittaker quotient πO of π. We define the Whittaker support WS(π) to be the set of maximal O among those for which ...

Twisted Whittaker models for metaplectic groups