{
  "abstract": "We prove the simple-object prediction of Shan--Yan--Zhao and a basis-preserving dual-cell realization for the distinguished vacuum block of the simple affine vertex algebras $L_{-1}(D_\\ell)$, $\\ell\\ge5$. The block has exactly $\\ell+1$ simple objects, indexed by the subregular affine left cell containing $s_0$. The proof combines a primitive-ideal inclusion, an independent exhaustion argument, and a finite-length step. A noncritical Sugawara lift supplies finite-dimensional weight-space detectors in the original Shan--Yan--Zhao category-$\\mathcal O$ block, so dévissage applies to its ordinary Grothendieck group. We then identify this group, basis by basis, with the $q=1$ specialization of the corresponding dual affine left-cell module. An injective signed normalized-character realization identifies the resulting image with the canonical dual-cell image in the completed singular-orbit module and hence supplies the corresponding abstract $\\widehat W$-module structure. We do not identify this action with a functorial action arising from affine twisting functors or Kashiwara--Tanisaki localization. The subregular inverse Kazhdan--Lusztig calculation of Bezrukavnikov--Kac--Krylov also yields uniform character formulas.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.11997",
  "author_total": 1,
  "authors": [
    {
      "name": "Sihai Jin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2bpjev94zzs3t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.11997",
  "fulltext_url": null,
  "id": "2bpjev94zzs3t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.11997",
  "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": "W7202396588",
  "pdf_url": "https://arxiv.org/pdf/2608.11997",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2bpjev94zzs3t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.11997",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.11997"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Subregular affine cells and the level $-1$ vertex algebra of type $D$",
  "title_text": "Subregular affine cells and the level −1 vertex algebra of type D",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/2bpjev94zzs3t",
  "venue": "arXiv",
  "versions": []
}