Hilbert series of representations of categories of G-sets

2024/04/30 by Philip Tosteson, Tosteson, Philip · 1 citation
Decision Sciences · Mathematics · #05A15 #18A25 #20C20 #Category Theory (math.CT) #Commutative Algebra (math.AC) #FOS: Mathematics #Fuzzy and Soft Set Theory #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2404.19610

openalex publication_date 2024/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a finite group. A contravariant functor from the category of finite free G-sets to vector spaces has an associated Hilbert series, which records the underlying sequence of Gⁿ representations, n ∈ \mathbb N. We prove that this Hilbert series is rational with denominator given by linear polynomials with coefficients in the field generated by the character table of G.

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