A root system is a reformulation, in terms of linear algebra, of the concept of a finite Euclidean reflection group. More exactly, it is a translation into linear algebra of the geometric configuration formed by the reflecting hyperplanes associated with a reflection group. This reformulation is extremely important. The use of linear algebra enables us to analyze finite reflection groups with great efficiency. All of Chapters 2, 3, 4 and 6 will be devoted to the justification of this remark.
KeywordsRoot System Irreducible Representation Linear Algebra Weyl Group Permutation Group
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