Take Lie group $G$ with some hypotheses (compact, connected, semi-simple); call $T$ its maximal torus, its Lie algebra $\operatorname{Lie}(G)=\mathbf g$, its Cartan subalgebra $\operatorname{Lie}(T)=\mathbf t \subset \mathbf g$ and its Weyl group $W=N(T)/T$.
Why does the complexified space of conjugacy classes in $\mathbf g$ $$\mathcal M=(\mathbf t \otimes \mathbf C)/W$$ give a special Kähler manifold $\mathcal M$, if this is true?