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arXiv · 2404.19610

Hilbert series of representations of categories of $G$-sets

Philip Tosteson
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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 $G^n$ representations, $n \in \mathbb N$. 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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Philip Tosteson. 2024-04-30. Hilbert series of representations of categories of $G$-sets. https://arxiv.org/abs/2404.19610

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