Let W be the Weyl group of a simple complex Lie group G. If T is a maximal torus of G then W has a graded representation on the cohomology of the flag variety G/T, which is well-known to be equivalent to the representation of W on its coinvariant algebra S_{W}. It has long been known that for certain integers d, the sums of homogeneous components of S_{W} of degrees congruent to k mod d for a fixed k may be expressed as induced representations of W. I shall generalise and explain this in terms of the "twisted invariant theory" of an arbitrary unitary reflection group. |