Date of Award

1-1-2020

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

College/School/Department

Department of Mathematics and Statistics

Content Description

1 online resource (vi, 106 pages) : illustrations.

Dissertation/Thesis Chair

Michael Stessin

Committee Members

Antun Milas, Alexandre Tchernev, Rongwei Yang

Keywords

Coxeter groups, Group theory, Weyl groups, Abelian groups

Subject Categories

Physical Sciences and Mathematics

Abstract

Determinantal varieties constructed by linear representations of Coxeter generators on afinite dimensional Hilbert space were shown to determine representations of non-exceptional finite Weyl groups up to unitary equivalence by Cuckovic, Stessin, and Tchernev. This result posed the question if something analogous could be established for affine Coxeter groups. Since it is well known that these groups are infinite in order, we only consider representations that are finite dimensional, and we establish results about the structure and combinatorics of each group and its respective representation. The main results established in this dissertation shows that determinantal varieties of a set of group elements, containing generators and other special elements of the groups, determine the character of finite dimensional representations of affine Weyl groups ˜Bn, ˜ Cn, and ˜Dn.

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