Séminaires : Séminaire d'Algèbre

The leitfaden of this talk will be the general problem of determining which invariants of a finite group G are determined by which piece of the representation category of G over a commutative ring R. In the first part of the talk, we will recall the information encoded by the monoidal category of complex representations and its (braided) auto-equivalences. By doing so we will stumble on a question concerning the connection between two types of rigidity associated to G. The first is given by the group of class-preserving outer automorphisms of G and the second is a birational invariant of the quotient variety V/G, where V is a faithful representation of G. The aim of the second part of the talk will be to present some new perspective on them. Thereafter, in the last part, we will explain how the situation changes when taking R to be a number field or its ring of integers. In particular, the role of the theory of arithmetic groups will be emphasized. All along the talk, we will mention some open questions and some recent contributions.

This talk will take place in hybrid mode at the Institut Henri Poincaré.