Hilbert series of representations of categories of $G$-sets
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914777757908992 |
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| author | Tosteson, Philip |
| author_facet | Tosteson, Philip |
| contents | 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 $G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_19610 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hilbert series of representations of categories of $G$-sets Tosteson, Philip Representation Theory Commutative Algebra Category Theory 05A15, 20C20, 18A25 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 $G$. |
| title | Hilbert series of representations of categories of $G$-sets |
| topic | Representation Theory Commutative Algebra Category Theory 05A15, 20C20, 18A25 |
| url | https://arxiv.org/abs/2404.19610 |