The University of Michigan Combinatorics Seminar


Abstract 

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.
