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