Charles B. Whittaker

Metaplectic Whittaker Functions and Crystals of Type B

Let n be an integer and let F be a nonarchimedean local field whose characteristic is not a prime dividing n. Let μk be the group of k-th roots of unity in the algebraic closure of F ; we assume that μ2n ⊂ F . Let G be a split, simply-connected semisimple algebraic group over F . We assume that G is actually defined over the ring o of integers in F in such a way that K = G(o) is a special maxim...

Whittaker Quantum

We show that closed, radiation-filled Friedmann-Robertson-Walker quantum universes of arbitrary factor ordering obey the Whittaker equation. We also present the formal Witten factorization as well as the double Darboux strictly isospectral scheme for the Whittaker equation. If in the " time-time " component of Einstein's equations for Friedmann-Robertson-Walker (FRW) universes ˙ a 2 + k = 8πG 3...

CS 626 Homework # 4 Charles B . Ward Due : Tuesday

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...

Mellin transforms of Whittaker functions

In this note we show that for an arbitrary semisimple Lie group and any admissible irreducible Banach representation the Mellin transforms of Whittaker functions extend to meromorphic functions. We determine the possible poles.