Coxeter Groups: Geometric Equivalence and Positive Definite Graphs

This lecture discusses the geometric equivalence of Coxeter groups with the same Coxeter graph, emphasizing the connection to positive definite matrices. It covers the proof of geometric equivalence using sets of simple roots, matrix definitions, and positive definiteness criteria. The lecture also explores the concept of a positive definite Coxeter graph and its implications in group theory, providing examples and theoretical insights.