Speaker: Johannes Schmitt (Bochum)
Title: Invariants in the Cohomology of the Complement of Quaternionic Reflection Arrangements
Abstract:
Let \(A\) be a hyperplane arrangement and \(G\) a finite group acting on \(A\). We are interested in the \(G\)-invariants of the ring \(H^*(M(A))\), that is, the rational, singular cohomology of the complement space \(M(A)\). Douglass, Pfeiffer and Röhrle determined the Poincaré polynomial of these invariants in the case of a complex reflection group \(G\) and the corresponding reflection arrangement \(A\). In this talk, we extend these results to quaternionic reflection groups. We collect the necessary foundations regarding "quaternionic reflection arrangements" and compute the Poincaré polynomials of the invariants of their cohomology. This is joint work with Lorenzo Giordani and Gerhard Röhrle.