{
  "abstract": "We prove the Kazhdan-Lusztig correspondence for the Lie superalgebra $\\mathfrak{osp}_{1|2n}$ at irrational levels, that is, we show the category $\\mathrm{KL}_k^{\\rm ev}(\\mathfrak{osp}_{1|2n})$ of finite-length even ordinary modules for the affine vertex operator superalgebra of $\\mathfrak{osp}_{1|2n}$ at level $k \\in \\mathbb{C} \\setminus \\mathbb{Q}$ is braided tensor equivalent to the category of finite-dimensional even weight modules for the quantum group of $\\mathfrak{osp}_{1|2n}$ at parameter $q = e^{πi/(2k+2n+1)}$. We also prove that ${\\rm KL}_k^{\\rm ev}(\\mathfrak{osp}_{1|2n})$ is braided tensor equivalent to the category ${\\rm KL}_\\ell^{\\rm ns}(\\mathfrak{so}_{2n+1})$ of finite-length ordinary modules with non-spinorial top level for the affine vertex operator algebra of $\\mathfrak{so}_{2n+1}$ at level $\\ell$ such that $ \\frac{1}{\\ell+ 2n-1} = \\frac{1}{2k+2n+1} + 1 \\ \\ ({\\rm mod}\\ 2\\mathbb Z).$ Consequently, by gluing vertex operator (super)algebras via tensor categories, we construct a few new families of simple conformal vertex (super)algebras, including the mixed kernel VOAs that were the missing ingredient for proving certain Feigin-Frenkel type dualities in previous work of the first-named author with Linshaw, Nakatsuka, and Sato.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28094",
  "author_total": 3,
  "authors": [
    {
      "name": "Thomas Creutzig"
    },
    {
      "name": "Robert McRae"
    },
    {
      "name": "Jinwei Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3yw7txv7cr35n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28094",
  "fulltext_url": null,
  "id": "3yw7txv7cr35n",
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  "landing_url": "https://arxiv.org/abs/2609.28094",
  "language": null,
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  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-th"
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    [
      "arxiv",
      "math-ph"
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    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.QA"
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      "arxiv",
      "math.RT"
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      "openalex",
      "2608|Algebraic structures and combinatorial models"
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  "openalex": "W7214146043",
  "pdf_url": "https://arxiv.org/pdf/2609.28094",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3yw7txv7cr35n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:56Z",
      "native_id": "2609.28094",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28094"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "The Kazhdan-Lusztig category of $\\mathfrak{osp}_{1|2n}$ at irrational levels",
  "title_text": "The Kazhdan-Lusztig category of osp_1|2n at irrational levels",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/3yw7txv7cr35n",
  "venue": "arXiv",
  "versions": []
}