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In mathematics, in particular the theory of Lie algebras, the Weyl group of a root system Φ is a subgroup of the isometry group of that root system. Specifically, it is the subgroup which is generated by reflections through the hyperplanes orthogonal to at least one of the roots, and as such is a finite reflection group. In fact it turns out that most finite reflection groups are Weyl groups. Abstractly, Weyl groups are finite Coxeter groups, and are important examples of these.
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