Coxeter Groups: Simple Roots and Reflections

This lecture focuses on the properties of the simple roots and simple reflections of a Coxeter group. The instructor explains the classification of finite Coxeter groups, emphasizing the uniqueness and basis of simple reflections. The lecture delves into the dependence of roots and the generation of all roots by simple reflections. The instructor demonstrates the process of mapping positive roots to simple roots and proves the possibility of linear independence. The lecture concludes with constructing a sequence of elements and terminating the process by hitting a finite set.