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Decomposition of principal series representations and Clebsch-Gordan coefficients
Descriptive
TitleInfo
Title
Decomposition of principal series representations and Clebsch-Gordan coefficients
Name
(type = personal)
NamePart
(type = family)
Zhang
NamePart
(type = given)
Zhuohui
NamePart
(type = date)
1989-
DisplayForm
Zhuohui Zhang
Role
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author
Name
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Miller
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Stephen David
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Stephen David Miller
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Advisory Committee
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chair
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Sahi
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Siddhartha
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Siddhartha Sahi
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internal member
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Lepowsky
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(type = given)
James
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James Lepowsky
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Advisory Committee
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internal member
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Pollack
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Aaron
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Aaron Pollack
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Advisory Committee
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Rutgers University
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degree grantor
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School of Graduate Studies
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Text
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theses
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2018
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2018-10
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2018
Place
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xx
Language
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eng
Abstract
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In this thesis, following a similar procedure developed by Buttcane and Miller in "Weights, raising and lowering operators, and K-types for automorphic forms on SL(3,R)" for SL(3,R), the (g,K)-module structures of the minimal principal series of real reductive Lie groups SU(2,1) and Sp(4,R) are described explicitly by realizing the representations in the space of K-finite functions on U(2). Moreover, by combining combinatorial techniques and contour integrations, this thesis introduces a method of calculating intertwining operators on the principal series. Upon restriction to each K-type, the matrix entries of intertwining operators are represented by Gamma-functions and Laurent series coefficients of hypergeometric series. The calculation of the (g,K)-module structure of principal series can be generalized to real reductive Lie groups whose maximal compact subgroup is a product of SU(2)'s and U(1)'s.
Subject
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Topic
Mathematics
Subject
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Topic
Lie groups
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Rutgers University Electronic Theses and Dissertations
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ETD_9254
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electronic resource
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1 online resource (114 pages : illustrations)
Note
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Ph.D.
Note
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Includes bibliographical references
Note
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by Zhuohui Zhang
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School of Graduate Studies Electronic Theses and Dissertations
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rucore10001600001
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doi:10.7282/t3-sv7e-jz28
Genre
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ETD doctoral
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Rights
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The author owns the copyright to this work.
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Name
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Zhang
GivenName
Zhuohui
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Permission or license
DateTime
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2018-09-27 19:09:47
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Zhuohui Zhang
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Affiliation
Rutgers University. School of Graduate Studies
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Author Agreement License
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I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
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2018-10-31
DateTime
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2019-10-31
Detail
Access to this PDF has been restricted at the author's request. It will be publicly available after October 31st, 2019.
Copyright
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
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2018-09-27T19:07:17
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2018-09-27T19:07:17
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