2026-09-20T04:42:18Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/901832026-06-17T14:43:44Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Benjamin Brubaker.
DeFranco, Mario A. (Mario Anthony)
Massachusetts Institute of Technology. Department of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2014-09-19T21:44:42Z
2014-09-19T21:44:42Z
2014
2014
http://hdl.handle.net/1721.1/90183
890210958
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2014.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 99-101).
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.
by Mario A. DeFranco.
Ph.D.
101 pages
eng
Massachusetts Institute of Technology
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.
http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
The unramified principal series of p-adic groups : the Bessel function
Thesis
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<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.</Abstract>
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