The unramified principal series of p-adic groups : the Bessel function
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2014.
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| Fformat: | Traethawd Ymchwil |
| Iaith: | eng |
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Massachusetts Institute of Technology
2014
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| Mynediad Ar-lein: | http://hdl.handle.net/1721.1/90183 |
| _version_ | 1826203329378648064 |
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| author | DeFranco, Mario A. (Mario Anthony) |
| author2 | Benjamin Brubaker. |
| author_facet | Benjamin Brubaker. DeFranco, Mario A. (Mario Anthony) |
| author_sort | DeFranco, Mario A. (Mario Anthony) |
| collection | MIT |
| description | Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2014. |
| first_indexed | 2024-09-23T12:35:13Z |
| format | Thesis |
| id | mit-1721.1/90183 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T12:35:13Z |
| publishDate | 2014 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/901832019-04-11T03:01:56Z The unramified principal series of p-adic groups : the Bessel function DeFranco, Mario A. (Mario Anthony) Benjamin Brubaker. Massachusetts Institute of Technology. Department of Mathematics. Massachusetts Institute of Technology. Department of Mathematics. Mathematics. 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. 2014-09-19T21:44:42Z 2014-09-19T21:44:42Z 2014 2014 Thesis http://hdl.handle.net/1721.1/90183 890210958 eng 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 101 pages application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. DeFranco, Mario A. (Mario Anthony) The unramified principal series of p-adic groups : the Bessel function |
| title | The unramified principal series of p-adic groups : the Bessel function |
| title_full | The unramified principal series of p-adic groups : the Bessel function |
| title_fullStr | The unramified principal series of p-adic groups : the Bessel function |
| title_full_unstemmed | The unramified principal series of p-adic groups : the Bessel function |
| title_short | The unramified principal series of p-adic groups : the Bessel function |
| title_sort | unramified principal series of p adic groups the bessel function |
| topic | Mathematics. |
| url | http://hdl.handle.net/1721.1/90183 |
| work_keys_str_mv | AT defrancomarioamarioanthony theunramifiedprincipalseriesofpadicgroupsthebesselfunction AT defrancomarioamarioanthony unramifiedprincipalseriesofpadicgroupsthebesselfunction |