Seminar

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.