{
  "abstract": "Given an oligomorphic group $G$ G and a measure $\\mu $ μ for $G$ G (in a sense that we introduce), we define a rigid tensor category $\\operatorname{\\underline{Perm}}(G; \\mu )$ of “permutation modules,” and, in certain cases, an abelian envelope $\\operatorname{\\underline{\\textup{Rep}}}(G; \\mu )$ of this category. When $G$ G is the infinite symmetric group, this recovers Deligne’s interpolation category. Other choices for $G$ G lead to fundamentally new tensor categories. For example, we construct the first known semi-simple pre-Tannakian categories in positive characteristic with super-exponential growth. One interesting aspect of our construction is that, unlike previous work in this direction, our categories are concrete: the objects are modules over a ring, and the tensor product receives a universal bi-linear map. Central to our constructions is a novel theory of integration on oligomorphic groups, which could be of more general interest. Classifying the measures on an oligomorphic group appears to be a difficult problem, which we solve in only a few cases.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "name": "Nate Harman",
      "orcid": "0000-0002-1048-6644"
    },
    {
      "name": "Andrew Snowden",
      "orcid": "0009-0004-9952-7714"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dhfkfmg8dxqbw.bib",
  "cited_by": 42,
  "doi": "10.1007/s00222-026-01452-2",
  "fulltext_url": null,
  "id": "dhfkfmg8dxqbw",
  "issns": [
    "0020-9910",
    "1432-1297"
  ],
  "landing_url": "https://doi.org/10.1007/s00222-026-01452-2",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W4223582430",
  "pdf_url": "https://link.springer.com/content/pdf/10.1007/s00222-026-01452-2.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": "Springer Science+Business Media",
  "ris": "https://research.draconitic.com/paper/dhfkfmg8dxqbw.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T13:20:59Z",
      "native_id": "W4223582430",
      "source": "openalex",
      "url": "https://doi.org/10.1007/s00222-026-01452-2"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2608|Algebraic structures and combinatorial models",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Oligomorphic groups and tensor categories",
  "title_text": "Oligomorphic groups and tensor categories",
  "type": "peer-reviewed",
  "updated_at": "2026-11-08T13:20:35Z",
  "url": "https://research.draconitic.com/paper/dhfkfmg8dxqbw",
  "venue": "Inventiones mathematicae",
  "versions": []
}