{
  "abstract": "In characteristic zero, we prove that the Tor algebras of the generic, symmetric, and skew-symmetric determinantal rings are Koszul with respect to a natural regrading. In particular, their Eilenberg--Moore spectral sequence degenerates, which allows us to explicitly determine the Poincaré series of their residue fields and answers a problem raised by Avramov. To do this, we construct the universal hook algebra and prove that it has a quadratic Gröbner basis and thus is Koszul. This leads to a new standard monomial construction of the irreducible polynomial GL-representations, alongside the Schur and Weyl functors, which is of independent interest.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12675",
  "author_total": 3,
  "authors": [
    {
      "name": "Steven V Sam"
    },
    {
      "name": "Keller VandeBogert"
    },
    {
      "name": "Jerzy Weyman"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9zvgxdf4bpg4n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12675",
  "fulltext_url": null,
  "id": "9zvgxdf4bpg4n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12675",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AC"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2602|Commutative Algebra and Its Applications"
    ]
  ],
  "openalex": "W7221539385",
  "pdf_url": "https://arxiv.org/pdf/2610.12675",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9zvgxdf4bpg4n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.12675",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12675"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Hook algebras and determinantal varieties",
  "title_text": "Hook algebras and determinantal varieties",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/9zvgxdf4bpg4n",
  "venue": "arXiv",
  "versions": []
}