Section: New Results

Resultant of an equivariant polynomial system with respect to the symmetric group

Participants : Laurent Busé, Anna Karasoulou.

Given a system of $n$ homogeneous polynomials in $n$ variables which is equivariant with respect to the canonical actions of the symmetric group of $n$ symbols on the variables and on the polynomials, we prove in [4] 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.