The attached picture is from Hitchin's Duke paper STABLE BUNDLES AND INTEGRABLE SYSTEMS. Let G be a semsimple complex Lie group and $P_1,P_2...P_k$ be a basis of homogeneous invariant polynomials in the ring of invariant polynomials of degree $d_i$ respectively. Then Hitchin claims the following is well known. Can someone give a proof of this?
