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arXiv · 2508.21713

Resultant of an equivariant polynomial system with respect to direct product of symmetric groups

Sonagnon Julien Owolabi·Ibrahim Nonkane·Joel Tossa
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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.

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Sonagnon Julien Owolabi, Ibrahim Nonkane, Joel Tossa. 2025-08-29. Resultant of an equivariant polynomial system with respect to direct product of symmetric groups. https://arxiv.org/abs/2508.21713

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