Separating Invariants for Two Copies of the Natural S_n-Action

2019/05/31 by Fabian Reimers, Reimers, Fabian · 2 citations
Computer Science · Mathematics · #13A50 #Algebraic Geometry and Number Theory #Coding theory and cryptography #Commutative Algebra (math.AC) #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1905.13608

openalex publication_date 2019/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This note provides a set of separating invariants for the ring of vector invariants K[V²]^S_n of two copies of the natural S_n-representation V = Kⁿ over a field of characteristic 0. This set is much smaller than generating sets of K[V²]^S_n. For n ≤ 4 we show that this set is minimal with respect to inclusion among all separating sets.

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