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Proof of Existence and Uniqueness of Simple Root Systems, Clarified

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.

Identiferoai:union.ndltd.org:siu.edu/oai:opensiuc.lib.siu.edu:theses-3811
Date01 December 2020
CreatorsHolt, William Ian
PublisherOpenSIUC
Source SetsSouthern Illinois University Carbondale
Detected LanguageEnglish
Typetext
Formatapplication/pdf
SourceTheses

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