Darstellungstheorietage and Nikolaus Conference 2013

Speaker: Götz Pfeiffer (Galway)

Title: On Descent Algebras and the Cohomology of Hyperplane Complements

Abstract: The descent algebra of a finite Coxeter group \(W\) can be used to decompose the group algebra of \(W\) in such a way that a simple relationship with the Orlik-Solomon algebra of the hyperplane arrangement of \(W\) becomes apparent. The summands in that decomposition are induced from linear characters of centralizers, one for each conjugacy class of \(W\). I will discuss this decomposition and the status of various conjectures relating to it. This is joint work with M. Bishop, J. M. Douglass and G. Röhrle.