Date of Award

Spring 5-2019

Document Type

Honors Thesis

Degree Name

Bachelor of Arts

Department

Mathematics and Statistics

Advisor/Committee Chair

Changlong Zhong, Ph.D.

Abstract

We begin this paper with a short survey on finite reflection groups. First we establish what a reflection in Euclidean space is. Then we introduce a root system, which is then partitioned into two sets: one of positive roots and one with negative roots. Th is articulates our understanding of groups generated by simple reflections. Furthermore, we develop our insight to Weyl groups and crystallographic groups before exploring crystallographic root systems. The section section of this paper examines the twisted group algebra along with the Demazure element Xi and the Demazure-Lusztig element Ti. Lastly, the third section of this paper computes such Xi and Ti in the case of S3 where S3 is the symmetric group Sn, n=3.

Included in

Algebra Commons

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