Abstract
In this chapter we classify crystallographic root systems. In view of the discussion in §9–5, we shall then have also achieved a classification of Weyl groups. As we have already mentioned in the introduction to Part III, the study of Weyl groups and crystallographic root systems uses the results about reflection groups from Chapters 1 through 8. In particular, the classification of Weyl groups and crystallographic root systems will turn out to be refinements of the classification of reflection groups obtained in Chapter 8.
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