PreprintCC BY 4.0arXiv
Resultant of an equivariant polynomial system with respect to the reflection group G(r,n)
Abstract
We consider systems of homogeneous multivariate polynomials equivariant under the complex reflection group G(r,n) = (ℤ/rℤ)n rtimes Sn. 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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BibTeX
@misc{owolabi2026resultant,
title = {{Resultant of an equivariant polynomial system with respect to the reflection group $G(r,n)$}},
author = {Sonagnon Julien Owolabi and Ibrahim Nonkané and Joel Tossa},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27886},
eprint = {2609.27886},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27886},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Resultant of an equivariant polynomial system with respect to the reflection group G(r,n)
AU - Sonagnon Julien Owolabi
AU - Ibrahim Nonkané
AU - Joel Tossa
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.27886
UR - https://arxiv.org/abs/2609.27886
AB - We consider systems of homogeneous multivariate polynomials equivariant under the complex reflection group G(r,n) = (ℤ/rℤ)^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.
ER -