Home
Resource
Decomposition of principal series representations and Clebsch-Gordan coefficients
PDF
PDF format is widely accepted and good for printing.
Plug-in required
PDF-1(700.38 kb)
Citation & Export
View Usage Statistics
Staff View

Citation & Export
Hide

Simple citation

Zhang, Zhuohui. Decomposition of principal series representations and Clebsch-Gordan coefficients. Retrieved from https://doi.org/doi:10.7282/t3-sv7e-jz28

Export

Click here for information about Citation Management Tools at Rutgers.

Statistics
Hide

Description

TitleDecomposition of principal series representations and Clebsch-Gordan coefficients
NameZhang, Zhuohui (author); Miller, Stephen David (chair); Sahi, Siddhartha (internal member); Lepowsky, James (internal member); Pollack, Aaron (outside member); Rutgers University; School of Graduate Studies
Date Created2018
Other Date2018-10 (degree)
SubjectMathematics, Lie groups
Extent1 online resource (114 pages : illustrations)
DescriptionIn 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.
NotePh.D.
NoteIncludes bibliographical references
Noteby Zhuohui Zhang
Genretheses, ETD doctoral
Persistent URLhttps://doi.org/doi:10.7282/t3-sv7e-jz28
Languageeng
CollectionSchool of Graduate Studies Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.
Version 8.5.5
Rutgers University Libraries - Copyright ©2024