Gus Lehrer (University of Sydney)

Friday 12th October, 12.05-12.55pm, Carslaw 373

The flag variety and twisted invariants of reflection groups

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.