The University of Michigan Combinatorics Seminar
Fall 2002
October 18, 4:10-5:00, 3866 East Hall

Equivariant Euler characteristics of discriminants of reflection groups

Graham Denham

University of Western Ontario


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 Cm. The virtual G x Cm 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.