Unramified Whittaker functions on p-adic loop groups

Mellin transforms of p-adic Whittaker functions

ON p-ADIC GENERALIZED WHITTAKER FUNCTIONS ON GSp(4)

Let G be a connected reductive algebraic group defined over a non-Archimedean local field F . The study of Whittaker functions on G has a long history. For example, if G = GL(2), an explicit formula for the Whittaker function is well-known (See [5]). Shintani proved an explicit formula for the case G = GL(n) and expressed it by Schur polynomials in [16]. Casselman and Shalika generalized Shinta...

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...

Fast arithmetic in unramified p-adic fields

Let p be prime and Zpn a degree n unramified extension of the ring of p-adic integers Zp. In this paper we give an overview of some very fast deterministic algorithms for common operations in Zpn modulo p . Combining existing methods with recent work of Kedlaya and Umans about modular composition of polynomials, we achieve quasi-linear time algorithms in the parameters n and N , and quasi-linea...

GENERALIZED SPHERICAL FUNCTIONS ON REDUCTIVE p-ADIC GROUPS

Let G be the group of rational points of a connected reductive p-adic group and let K be a maximal compact subgroup satisfying conditions of Theorem 5 from Harish-Chandra (1970). Generalized spherical functions on G are eigenfunctions for the action of the Bernstein center, which satisfy a transformation property for the action of K. In this paper we show that spaces of generalized spherical fu...