Alexander Veselov (Loughborough University)
Consider the natural action of a Coxeter group G on the complement MG to the complexified reflection hyperplanes and ask what is the corresponding action on the total cohomology H*(MG, C). When G is the symmetric group Sn, the space MG is the configuration space of n distinct points on the plane, whose cohomology algebra was computed by Arnol'd and the action was investigated by Lehrer and Solomon.
I will give an explicit description of this action for any finite Coxeter group G in terms of the special involutions in G, which I am going to introduce.
The proofs are based on simple topological arguments involving the generalised Lefschetz fixed point formula. I will discuss also the relations with the cohomology of the Brieskorn's braid groups. The talk is based on the recent results by G. Felder and the speaker.