Date of Award

Spring 5-8-2020

Level of Access

Open-Access Thesis

Degree Name

Master of Arts (MA)

Department

Mathematics

Advisor

Tyrone Crisp

Second Committee Member

Andrew Knightly

Third Committee Member

Julian Rosen

Abstract

The main result of this thesis is that there exists a positive, self-adjoint Hopf (PSH) algebra structure in the representation theory of a certain family of groups. This new construction is inspired directly by Andrey Zelevinsky’s discovery of such a structure in the representation theory of the symmetric groups. Zelevinsky’s work Representations of finite classical groups: a Hopf algebra approach gives an account of this. We will walk through Zelevinsky’s work in this field in detail, and then follow up with the construction on the groups in question. We will develop the necessary theory along the way, with the reader assumed to be familiar with the basic properties of groups and rings. The notion of categories, functors, and Grothendieck groups will be useful, but knowledge of these concepts is not necessary for the reading of this thesis.

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