Coxeter Groups: Simple Reflections and Conjugacy

This lecture delves into Coxeter groups, focusing on the theorem that an element sending all simple roots to simple roots is the identity. The instructor proves that any element in a Coxeter group can be expressed as a product of simple reflections and explores the conjugacy of reflections to simple reflections. The lecture also discusses the independence of certain elements on the initial choice of generators and the relationship between different elements in the group. Various examples and proofs are provided to illustrate these concepts.