Abstract
This chapter gives a first introduction to the theory of Coxeter groups. In Sect. 1.1 we define Coxeter groups, discuss the Coxeter groups of type ABCD, and give the classification of finite Coxeter groups. We also discuss diagrammatic ways to present elements in type A and B. In Sect. 1.2 we discuss the fundamentals of Coxeter groups: the length function, descent sets, the exchange condition, the longest element, Matsumoto’s theorem, and Bruhat order.
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