  Polynomial invariants are fundamental objects in analysis on Lie groups and
symmetric spaces. Invariant differential operators on symmetric spaces are
described by Weyl group invariant polynomial. In this article we give a simple
criterion that ensure that the restriction of invariant polynomials to
subspaces is surjective. In another paper we will apply our criterion to
problems in Fourier analysis on projective/injective limits, specifically to
theorems of Paley--Wiener type.
