Separating invariants for multisymmetric polynomials

Lopatin, Artem; Reimers, Fabian

doi:10.1090/proc/15292

Separating invariants for multisymmetric polynomials
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by Artem Lopatin and Fabian Reimers

Proc. Amer. Math. Soc. 149 (2021), 497-508

DOI: https://doi.org/10.1090/proc/15292

Published electronically: December 14, 2020

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Abstract:

This article studies separating invariants for the ring of multisymmetric polynomials in $m$ sets of $n$ variables over an arbitrary field $\mathbb {K}$. We prove that in order to obtain separating sets it is enough to consider polynomials that depend only on $\lfloor \frac {n}{2} \rfloor + 1$ sets of these variables. This improves a general result by Domokos about separating invariants. In addition, for $n \leq 4$ we explicitly give minimal separating sets (with respect to inclusion) for all $m$ in case $\text {char}(\mathbb {K}) = 0$ or $\text {char}(\mathbb {K}) > n$.

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