If "T" is a maximal torus in a compact Lie group "G", one can define a root system as follows. The roots are the weights for the adjoint action of "T" on the complexified Lie algebra of "G". To be more explicit, let formula_5 denote the Lie algebra of "T", let formula_3 denote the Lie algebra of formula_7, and let formula_8 denote the complexification of formula_3. Then we say that an element formula_10 is a root for "G" relative to "T" if formula_11 and there exists a nonzero formula_12 such that