Section: New Results

Invariantization of symmetric polynomial systems

Participants : Mathieu Collowald, Evelyne Hubert.

Assuming the variety of a set of polynomials is invariant under a group action, we provide a set of invariants that define the same variety. The contribution is about infinite algebraic groups, the case of finite group being previously known. We introduce for those a new concept of algebraic invariantization. It is based on the construction of rational invariants by Hubert and Kogan [14] , a construction for which we provide here new simplified proofs.