  Suppose that G is a finite, unitary reflection group acting on a complex
vector space V and X is the fixed point subspace of an element of G. Define N
to be the setwise stabilizer of X in G, Z to be the pointwise stabilizer, and
C=N/Z. Then restriction defines a homomorphism from the algebra of G-invariant
polynomial functions on V to the algebra of C-invariant functions on X.
Extending earlier work by Douglass and Roehrle for Coxeter groups, we
characterize when the restriction mapping is surjective for arbitrary unitary
reflection groups G in terms of the exponents of G and C, and their reflection
arrangements. A consequence of our main result is that the variety of G-orbits
in the G-saturation of X is smooth if and only if it is normal.
