The unramified principal series of p-adic groups : the Bessel function
Name
890210958-MIT.pdf
Description
Full printable version
Size
2.31 MB
Format
Adobe PDF
Checksum (MD5)
b05f3c67754e1d0d4604eebb579097df
Author(s)
DeFranco, Mario A. (Mario Anthony)
Advisor(s)
Benjamin Brubaker.
Date Issued
2014
Publisher
Massachusetts Institute of Technology
Abstract
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.
Description
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2014.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 99-101).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
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