Equivariant Euler characteristics of discriminants of reflection groups

Let G be a finite, complex reflection group acting on a complex vector space V, and d its disciminant polynomial. The fibres of d admit commuting actions of G and a cyclic group C_m. The virtual G x C_m character given by the Euler characteristic of a fibre is a refinement of the zeta function of the geometric monodromy, calculated by Denef and Loeser in 1995. Recent enhancements to Springer's theory of regular elements make it possible to describe this virtual character explicitly, in terms of a certain poset of subgroups of G. This poset is a diagram invariant G, in the sense of Broué, Malle, and Rouquier. I will attempt to justify its interest and significance.