Weyl group of a compact Lie group

Summary

Let $G$ be a compact connected Lie group with maximal torus $T$. Its Weyl group is the finite group $N_G(T)/T$, where $N_G(T)$ is the normaliser of $T$. It acts on $T$ by conjugation and records how elements of $T$ can be conjugate in $G$. It is isomorphic to the Weyl group of the root system of $G$, which is generated by reflections. It appears in the Weyl integration and character formulas.