Resultant of an equivariant polynomial system with respect to direct product of symmetric groups
Sonagnon Julien Owolabi, Ibrahim Nonkane, Joel Tossa
Published: 2025/8/29
Abstract
In this note, we consider the resultant of systems of homogeneous multivariate polynomials which are equivariant under the action of direct product of two symmetric groups. We establish a decomposition formula for the resultant of such systems. Thanks to that decomposition formula we prove that the discriminant of an invariant multivariate homogeneous polynomial under a direct product of symmetric groups splits into smaller resultants that are easier to compute.