The unramified principal series of p-adic groups : the Bessel function

Let G be a connected reductive group with a split maximal torus defined over a nonarchimedean local field. I evaluate a matrix coefficient of the unramified principal series of G known as the "Bessel function" at torus elements of dominant coweight. I show that the Bessel function shares many properties with the Macdonald spherical function of G, in particular the properties described in Casselman's 1980 evaluation of that function. The analogy I demonstrate between the Bessel and Macdonald spherical functions extends to an analogy between the spherical Whittaker function, evaluated by Casselman and Shalika in 1980, and a previously unstudied matrix coefficient.

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mathematics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2014

Author dc:creator

• DeFranco, Mario A. (Mario Anthony)

Advisor dc:contributor.advisor

• Benjamin Brubaker.

• Mathematics.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/90183

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/90183