Chevalley restriction theorem

In the mathematical theory of Lie groups, the Chevalley restriction theorem describes functions on a Lie algebra which are invariant under the action of a Lie group in terms of functions on a Cartan subalgebra.
Statement.
Chevalley's theorem requires the following notation:
Chevalley's theorem asserts that the restriction of polynomial functions induces an isomorphism
Proofs.
 gives a proof using properties of representations of highest weight. give a proof of Chevalley's theorem exploiting the geometric properties of the map formula_2.