Graduate Algebra Symposium
Invariants and Arrangements of Finite Complex Reflection Groups
Suppose G is a finite complex reflection group acting on a complex vector space V, and X is a subspace of V in the lattice of the arrangement of G. Define N and Z to be the setwise and pointwise stabilizers, respectively, of X in G. Then restriction from V to X defines a homomorphism from the algebra of G-invariant polynomial functions on V to the algebra of N/Z-invariant polynomial functions on X. In this talk I will first give a brief introduction to complex reflection groups, their hyperplane arrangements, and their invariants. Then I will describe a simple characterization of when this restriction mapping is surjective in terms of the exponents of G and N/Z and their reflection arrangements. This extends earlier work by Douglass and Roehrle when G is a Coxeter group.