Tuesday, June 4, 14:00, 7.527
Götz Pfeiffer (NUI Galway), On computations in the Orlik-Solomon
algebra of a reflection arrangement.
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.