Conjugacy Classes as the Weyl Quotient of a Maximal Torus identifies how maximal tori control the structure and conjugacy theory of compact Lie groups. In concrete terms, it formalizes the statement that let be a compact connected Lie group, let be a maximal torus, and let W:=NG(T)/T be the Weyl group, acting on by conjugation: for and , (nT) t:=ntn^-1..