Date of Award

12-1-2020

Degree Name

Master of Science

Department

Mathematics

First Advisor

Kocik, Jerzy

Abstract

Humphreys (1990) defines a simple root system for a finite reflection group which is an important concept fundamental to the understanding of reflection groups as well as Coxeter complexes and Coxeter groups. The proof that Humphreys uses to establish the existence and uniqueness of these systems follows an indirect method that left portions of the proof as exercises to the reader. I present a more complete and direct proof using different organization and methods.

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