Coxeter Groups: Generators and Relations

This lecture covers the concept of Coxeter groups, focusing on the generators and relations within these groups. The presentation includes the definition of a Coxeter group, the free group generated by a set of symbols, and the notion of reduced words. It also discusses Iwahori's lemma and the presentation of groups by generators and relations, emphasizing the uniqueness of the choice of generators. The lecture concludes with the application of these concepts to the dihedral group and the universal property of free groups.