Symmetric ideals of the infinite polynomial ring

2021/07/27 by Nagpal, Rohit, Snowden, Andrew · 3 citations
#Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2107.13027

Abstract

Let R=C[ξ₁,ξ₂,…] be the infinite variable polynomial ring, equipped with the natural action of the infinite symmetric group \mathfrakS. We classify the \mathfrakS-primes of R, determine the containments among these ideals, and describe the equivariant spectrum of R. We emphasize that \mathfrakS-prime ideals need not be radical, which is a primary source of difficulty. Our results yield a classification of \mathfrakS-ideals of R up to copotency. Our work is motivated by the interest and applications of \mathfrakS-ideals seen in recent years.

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• On representations of permutation groups and orbit categories
• Symmetric modules over the infinite polynomial ring I: nilpotent quotients
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