Type: Seminar

Modified: Fri 10 Mar 2017 1727

Distribution: World

Expiry: 21 Apr 2017

CalTitle1: Algebra Seminar: Root systems for complex reflection groups

Auth: kevinc@pkevinc.pc (assumed)

Ruth Corran (American University of Paris) Friday 17 March, 12-1pm, Place: Carslaw 375 Title: Root systems for complex reflection groups. Abstract: I will speak about joint work with Michel Broue and Jean Michel, motivated by questions coming from the Spetses project. We define a Z_k-root system for a complex reflection group on a k-vector space V, where Z_k is the ring of integers of a number field, k. A root is no longer a vector, but something like a rank one Z_k-module of V. Our definition has natural consequences; for example, restricting in the obvious way to a parabolic subgroup gives rise to a new root system. In this way, for example, Z[i]-root systems naturally arise for Weyl groups of type B; including one distinct from the Weyl types B and C. We classify root systems (and root and coroot lattices) for complex reflection groups, present Cartan matrices and observe that for spetsial groups, the connection index has a property which generalizes the situation in Weyl groups.