  Suppose that W is a finite, unitary, reflection group acting on the complex
vector space V and X is a subspace of V. Define N to be the setwise stabilizer
of X in W, Z to be the pointwise stabilizer, and C=N/Z. Then restriction
defines a homomorphism from the algebra of W-invariant polynomial functions on
V to the algebra of C-invariant functions on X. In this note we consider the
special case when W is a Coxeter group, V is the complexified reflection
representation of W, and X is in the lattice of the arrangement of W, and give
a simple, combinatorial characterization of when the restriction mapping is
surjective in terms of the exponents of W and C. As an application of our
result, in the case when W is the Weyl group of a semisimple, complex, Lie
algebra, we complete a calculation begun by Richardson in 1987 and obtain a
simple combinatorial characterization of regular decomposition classes whose
closure is a normal variety.
