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arXiv · 2112.10207

On the non primality of certain symmetric ideals

Hyung Kyu Jun
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Abstract

Let $R =k[x_1, \cdots, x_n,\cdots]$ be the infinite variable polynomial ring equipped with the natural $\mathfrak{S}_\infty$ action, where $k$ is a field of characteristic zero. In recent work \cite{NS21}, Nagpal--Snowden gave an indirect proof that $\mathfrak{S}_\infty$-ideal generated by $(x_1-x_2)^{2n}$ is not $\mathfrak{S}_\infty$-prime. In this paper, we give a direct proof, with explicit elements. We further formulate some conjectures on possible generalizations of the result.

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Hyung Kyu Jun. 2021-12-19. On the non primality of certain symmetric ideals. https://arxiv.org/abs/2112.10207

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