Representation Theory of Real Reductive Groups

Author: Shang, Zhengyuan (John)

Year: 2021

Degree: Senior thesis (Major)

Advisor: Campbell, Christopher J.

Committee Members: Zhu, Xinwen; Flach, Matthias; Campbell, Christopher J.

Option: Mathematics

DOI: 10.7907/awt4-pz48

Abstract

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).

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• shang_zhengyuan_2021.pdf (application/pdf)