Abstract
In this chapter, we associate a canonical bilinear form to a finite Coxeter system and study its properties. The construction is motivated by the relation between finite reflection groups and Coxeter systems developed in §6–2. The main result of this chapter is that the bilinear form associated to a Coxeter system is always positive definite. In Chapter 8, we shall use the positive definiteness of this bilinear form to classify both finite Coxeter systems and finite Euclidean reflection groups.
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