Seminar Algebra and Geometry: Émilie Dufresne (Universität Basel)

Well-behaved separating algebras

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. One of the appeals of this new approach is that separating invariants can have better structural and computational properties than the ring of invariants. For example, there always exist a finite separating set, no matter the group. In this talk, we study well-behaved separating algebras for invariants of representations of finite groups. In particular, we show that if there exists a polynomial separating algebra, the the group action must be generated by (pseudo-)reflections.

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