{
  "abstract": "We determine the defining ideal of the simple affine vertex algebra $L_{2-\\ell}(\\mathfrak{so}_{2\\ell})$ for every odd $\\ell\\ge5$. Perše's quadratic singular vector alone generates the maximal ideal of the universal affine vertex algebra at this level. Together with the established even-rank presentation, this gives a complete parity-dependent description of this type-$D$ collapsing family at $k=2-\\ell$: one quadratic generator in odd rank, and a quadratic generator together with two Pfaffian generators in even rank. The proof establishes a rank reduction for the quadratic quotients under minimal Drinfeld--Sokolov reduction, valid in both parities. Nonvanishing of reduction on nonzero graded subquotients then lifts simplicity along the odd-rank chain from the known base case $D_3\\cong A_3$ at level $-1$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12706",
  "author_total": 1,
  "authors": [
    {
      "name": "Sihai Jin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fbhat8t09cwgn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12706",
  "fulltext_url": null,
  "id": "fbhat8t09cwgn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12706",
  "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": "W7212593613",
  "pdf_url": "https://arxiv.org/pdf/2609.12706",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fbhat8t09cwgn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.12706",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12706"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Odd-rank maximal ideals at collapsing levels of type $D$",
  "title_text": "Odd-rank maximal ideals at collapsing levels of type D",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/fbhat8t09cwgn",
  "venue": "arXiv",
  "versions": []
}