Resultant of an equivariant polynomial system with respect to the reflection group $G(r,n)$
Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214186438