Skip to Main Content
Frequently Asked Questions
Submit an ETD
Global Search Box
Need Help?
Keyword Search
Participating Institutions
Advanced Search
School Logo
Files
File List
Poderzay with signature.pdf (369.21 KB)
ETD Abstract Container
Abstract Header
Principal Series Representations of
GL
(2) Over Finite Fields
Author Info
Poderzay, Regina Carmella
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=ysu1527607113143289
Abstract Details
Year and Degree
2018, Master of Science in Mathematics, Youngstown State University, Department of Mathematics and Statistics.
Abstract
The goal of this thesis is to construct the principal series representations of
GL
(2). We do this in three parts. The aim of Part II is to become acquinted with representation theory. We observe rudimentary results and examples using prerequisite knowledge from linear algebra and group theory. We begin Part III by inducing new representations from old ones. A key component in the classification of induced representations is Mackey’s theorem. A generous portion of this thesis is dedicated to the proof of Mackey’s theorem. At last is Part IV where we construct the principal series representations. This constuction is motivated by the Bruhat decomposition of
GL
(2) into the Borel subgroup and is achieved by counting the conjugacy classes of
GL
2
(𝔽
q
).
Committee
Thomas Madsen, PhD (Committee Chair)
Neil Flowers, PhD (Committee Member)
Thomas Wakefield, PhD (Committee Member)
Pages
58 p.
Subject Headings
Mathematics
Keywords
representation theory
;
classification of irreducible representations
;
principal series representations
;
Mackey theory
Recommended Citations
Refworks
EndNote
RIS
Mendeley
Citations
Poderzay, R. C. (2018).
Principal Series Representations of
GL
(2) Over Finite Fields
[Master's thesis, Youngstown State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1527607113143289
APA Style (7th edition)
Poderzay, Regina.
Principal Series Representations of
GL
(2) Over Finite Fields.
2018. Youngstown State University, Master's thesis.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=ysu1527607113143289.
MLA Style (8th edition)
Poderzay, Regina. "Principal Series Representations of
GL
(2) Over Finite Fields." Master's thesis, Youngstown State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1527607113143289
Chicago Manual of Style (17th edition)
Abstract Footer
Document number:
ysu1527607113143289
Download Count:
792
Copyright Info
© 2018, all rights reserved.
This open access ETD is published by Youngstown State University and OhioLINK.