Graduate Thesis Or Dissertation

 

Type-free Approaches to Supercharacter Theories of Unipotent Groups Public Deposited

Downloadable Content

Download PDF
https://scholar.colorado.edu/concern/graduate_thesis_or_dissertations/z603qx442
Abstract
  • Supercharacter theories are a relatively new tool in studying the representation theory of unipotent groups over finite fields. In this thesis I present two new approaches to constructing supercharacter theories of finite unipotent groups. The first method utilizes group actions to construct supercharacter theories of the unipotent orthogonal, symplectic and unitary groups. The second technique is via the method of little groups, which describes the irreducible characters of a semidirect product with an abelian normal subgroup in terms of the irreducible characters of the factor groups. Motivated by these constructions, I produce supercharacter theories for a large collection of unipotent matrix groups and construct a Hopf monoid on the supercharacters.
Creator
Date Issued
  • 2014
Academic Affiliation
Advisor
Committee Member
Degree Grantor
Commencement Year
Subject
Last Modified
  • 2019-11-16
Resource Type
Rights Statement
Language

Relationships

Items