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arXiv · 2609.27886

Resultant of an equivariant polynomial system with respect to the reflection group $G(r,n)$

Sonagnon Julien Owolabi·Ibrahim Nonkané·Joel Tossa
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Abstract

We consider systems of homogeneous multivariate polynomials equivariant under the complex reflection group $G(r,n) = (\mathbb{Z}/r\mathbb{Z})^n \rtimes S_n$. Using divided differences indexed by partitions of $n$, we establish a decomposition formula expressing the resultant of such a system as a product of resultants of smaller, partition-indexed subsystems. Combining this with the classical resultant--discriminant relation, we show that the discriminant of a $G(r,n)$-invariant homogeneous polynomial splits explicitly into a product of resultants of smaller subsystems, considerably easier to compute; we illustrate both decompositions with worked examples.

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Sonagnon Julien Owolabi, Ibrahim Nonkané, Joel Tossa. 2026-08-20. Resultant of an equivariant polynomial system with respect to the reflection group $G(r,n)$. https://arxiv.org/abs/2609.27886

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