MSRI - Separating invariants and finite reflection groups

Time:	11:30AM - 12:15PM
Location:	MSRI, Simons Auditorium
Speaker:	Emilie Dufresne
Abstract:	The study of separating invariants is a new trend in Invariant Theory and a return to its roots: invariants as a classification tool. Rather than considering the whole ring of invariants, one considers a separating set, that is, a set of invariants whose elements separate any two points which can be separated by invariants. In this talk, we focus on representations of finite groups. We show that if there exists a polynomial separating algebra, the the group action must be generated by (pseudo-)reflections. This produces a new, simpler proof of the classical result of Serre that if the ring of invariants is polynomial then the group action must be generated by (pseudo-)reflections.