Arboreal tensor categories
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929280398655488 |
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| author | Harman, Nate Nekrasov, Ilia Snowden, Andrew |
| author_facet | Harman, Nate Nekrasov, Ilia Snowden, Andrew |
| contents | We introduce some new symmetric tensor categories based on the combinatorics of trees: a discrete family $\mathcal{D}(n)$, for $n \ge 3$ an integer, and a continuous family $\mathcal{C}(t)$, for $t \ne 1$ a complex number. The construction is based on the general oligomorphic theory of Harman--Snowden, but relies on two non-trivial results we establish. The first determines the measures for the class of trees, and the second is a semi-simplicity theorem. These categories have some notable properties: for instance, $\mathcal{C}(t)$ is the first example of a 1-parameter family of pre-Tannakian categories of superexponential growth that cannot be obtained by interpolating categories of moderate growth. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_06660 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Arboreal tensor categories Harman, Nate Nekrasov, Ilia Snowden, Andrew Representation Theory We introduce some new symmetric tensor categories based on the combinatorics of trees: a discrete family $\mathcal{D}(n)$, for $n \ge 3$ an integer, and a continuous family $\mathcal{C}(t)$, for $t \ne 1$ a complex number. The construction is based on the general oligomorphic theory of Harman--Snowden, but relies on two non-trivial results we establish. The first determines the measures for the class of trees, and the second is a semi-simplicity theorem. These categories have some notable properties: for instance, $\mathcal{C}(t)$ is the first example of a 1-parameter family of pre-Tannakian categories of superexponential growth that cannot be obtained by interpolating categories of moderate growth. |
| title | Arboreal tensor categories |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2308.06660 |