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The Weyl group of a root system is a subgroup generated by reflections through the hyperplanes orthogonal to the roots.

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Weyl group action on maximal tori

Let $G$ be a semisimple algebraic group over the complex numbers and we fix a maximal torus $T$. Let $w\in W$ be an element in the Weyl group, and let $T^{w}$ be the elements in $T$ that are fixed by …
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