Carslaw 375: Corran -- Root systems for complex reflection groups

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.