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 . References Lie groups Lie algebras Representation theory Algebraic geometry