Section: New Results
Resultant of an equivariant polynomial system with respect to the symmetric group
Participants : Laurent Busé, Anna Karasoulou.
Given a system of homogeneous polynomials in variables which is equivariant with respect to the canonical actions of the symmetric group of symbols on the variables and on the polynomials, we prove in  that its resultant can be decomposed into a product of several smaller resultants that are given in terms of some divided differences. As an application, we obtain a decomposition formula for the discriminant of a multivariate homogeneous symmetric polynomial.