Coxeter groups arise as a generalization of groups generated by reflexions. They are closely connected to Lie algebras and Hecke algebras. In fact, every Weyl group can be realized as a Coxeter group. In this talk we will introduce Coxeter groups with a view towards combinatorical applications and an emphasis on the intuition that arises from studying reflexion groups as a concrete example of Coxeter groups.
In particular, we will discuss
(1) The pictorial representation and classification of Coxeter groups using Coxeter graphs
(2) The Exchange Condition, a defining combinatorial property of Coxeter groups
(3) The Bruhat order, a partial ordering of Coxeter groups
Additionally, this talk will serve as an introduction to next week's talk on Hecke algebras.