Separating invariants for multisymmetric polynomials

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 $n\le 4$ we explicitly give minimal separating sets (with respect to inclusion) for all $m$ in case $\text{char}(\mathbb{K})=0$ or $\text{char}(\mathbb{K})>n$.

12 pages, accepted for publication in Proc AMS

Cited by in corpus (3)

• Separating invariants over finite fields
• Separating G_2-invariants of several octonions
• Classification of G_2-orbits for pairs of octonions