Separating invariants for multisymmetric polynomials
Authors:
Artem Lopatin and Fabian Reimers
Journal:
Proc. Amer. Math. Soc. 149 (2021), 497-508
MSC (2020):
Primary 13A50, 16R30, 20B30
DOI:
https://doi.org/10.1090/proc/15292
Published electronically:
December 14, 2020
MathSciNet review:
4198060
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Abstract | References | Similar Articles | Additional Information
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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Additional Information
Artem Lopatin
Affiliation:
Department of Mathematics, State University of Campinas, 651 Sergio Buarque de Holanda, 13083-859 Campinas, SP, Brazil
MR Author ID:
740650
Email:
artem\textunderscore lopatin@yahoo.com
Fabian Reimers
Affiliation:
Department of Mathematics, Technische Universität München, Zentrum Mathematik - M11, Boltzmannstr. 3, 85748 Garching, Germany
MR Author ID:
1271373
ORCID:
0000-0003-4552-8186
Email:
reimers@ma.tum.de
Keywords:
Invariant theory,
separating invariants,
symmetric group,
multisymmetric polynomials
Received by editor(s):
November 12, 2019
Received by editor(s) in revised form:
April 9, 2020
Published electronically:
December 14, 2020
Additional Notes:
The first author was supported by FAPESP 2019/10821-8. We are grateful for this support.
Communicated by:
Jerzy Weyman
Article copyright:
© Copyright 2020
American Mathematical Society