Tuesday, June 4, 14:00, 7.527

Götz Pfeiffer (NUI Galway), On computations in the Orlik-Solomon algebra of a reflection arrangement.

Abstract:
The Orlik-Solomon algebra of a hyperplane arrangement is a quotient of the exterior algebra of the hyperplanes. In the case of an arrangement whose hyperplanes are the reflecting hyperplanes of the reflections of a finite Coxeter group W, the Orlik-Solomon algebra A(W) is a module for W of dimension |W|. In this talk, I will discuss data structures and algorithms for efficient computations in this module. As an application, an explicit basis for the space of W-invariants of A(W) can determined for all the exceptional types of irreducible finite Coxeter groups W, thereby settling the remaining cases of a conjecture of Felder and Veselov. This is joint work with Gerhard Roehrle and Matt Douglass.