Date of Award
Level of Access Assigned by Author
Master of Arts (MA)
Second Committee Member
Third Committee Member
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.
Hill, Caleb Kennedy, "Hopf Algebras in the Representation Theory of Combinatorial//Families of Groups" (2020). Electronic Theses and Dissertations. 3213.