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Representation Theory of Real Reductive Groups


Shang, Zhengyuan (John) (2021) Representation Theory of Real Reductive Groups. Senior thesis (Major), California Institute of Technology. doi:10.7907/awt4-pz48.


The representation theory of Lie groups has connections to various fields in mathematics and physics. In this thesis, we are interested in the classification of irreducible admissible complex representations of real reductive groups. We introduce two approaches through the local Langlands correspondence and the Beilinson-Bernstein localization respectively. Then we investigate the connection between these two classifications for the group GL(2, R).

Item Type:Thesis (Senior thesis (Major))
Subject Keywords:Representation Theory
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Awards:Fredrick J. Zeigler Memorial Award, 2020.
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Campbell, Christopher J.
Thesis Committee:
  • Zhu, Xinwen (chair)
  • Flach, Matthias (co-chair)
  • Campbell, Christopher J.
Defense Date:14 May 2021
Record Number:CaltechTHESIS:06012021-050728468
Persistent URL:
Shang, Zhengyuan (John)0000-0002-8823-9483
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:14216
Deposited By: Zhengyuan Shang
Deposited On:01 Jun 2021 22:04
Last Modified:03 Nov 2021 20:26

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