{
  "abstract": "We study typical representations of an admissible type I algebraic supergroup $G$. We prove that, for a dominant weight $λ$, the induced supermodule $H^0_G(λ)$ is simple if and only if $λ$ is typical and the induced module $H^0_{G_{\\mathrm{ev}}}(λ)$ for the even subgroup $G_{\\mathrm{ev}}$ is simple. We establish equivalences between typical blocks for $G$ and blocks for $G_{\\mathrm{ev}}$, and give a projectivity criterion for Kac modules over every Frobenius kernel. For connected $SpO(2\\ell|2)$ over an algebraically closed field of odd characteristic, we classify all simple projective supermodules over Frobenius kernels.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23055",
  "author_total": 1,
  "authors": [
    {
      "name": "Taiki Shibata"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d555h198xy8j1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23055",
  "fulltext_url": null,
  "id": "d555h198xy8j1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23055",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.QA"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7222960784",
  "pdf_url": "https://arxiv.org/pdf/2610.23055",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d555h198xy8j1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.23055",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23055"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Typical representations of admissible type I algebraic supergroups",
  "title_text": "Typical representations of admissible type I algebraic supergroups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/d555h198xy8j1",
  "venue": "arXiv",
  "versions": []
}