A Weyl group is a specific kind of group associated with a root system in the theory of algebraic groups. It consists of the symmetries that preserve the structure of the root system and acts as an essential tool in understanding the representation theory of semisimple Lie algebras and algebraic groups. This group captures how reflections across hyperplanes defined by roots can rearrange the roots while preserving their relationships, providing deep insights into the geometric and algebraic properties of algebraic groups.
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