As indicated in the preface, the first systematic account of finite reflection groups was given by Coxeter  in 1934, following shortly after E. Cartan utilized the groups in his study of Lie groups and their associated Lie algebras. Coxeter classified not only the finite reflection groups, but also the infinite discrete groups generated by (affine) reflections. The infinite groups were likewise classified in terms of their Coxeter graphs.
KeywordsSimple Group Weyl Group Coxeter Group Chevalley Group Fundamental Region
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