{
  "abstract": "Arakawa and Moreau constructed explicit singular vectors in a family of negative-level universal affine vertex algebras of types $D$ and $E$ and conjectured that the ideals generated by these vectors are maximal. Previous work established the $n=0$ cases for $D_4$, $E_6$, $E_7$, and $E_8$, as well as the level $-2$ case for $D_\\ell$ with $\\ell\\geq 5$. We prove all the remaining cases: the level $-1$ case for $D_\\ell$ with $\\ell\\geq 5$, and the negative-level cases with $n>0$ for $D_4$, $E_6$, $E_7$, and $E_8$. Together with the previously known results, this completes Arakawa--Moreau Conjecture 1. The proof determines the images of the prescribed singular vectors under minimal Drinfeld--Sokolov reduction and establishes simplicity of the reduced quotients by combining a Ramond--Zhu algebra argument, a Casimir-gap argument, and Li's spectral flow. Exactness and a nonvanishing theorem for the reduction functor then lift simplicity to the corresponding affine quotients. We also formulate a general maximality principle based on minimal reduction, give an alternative reduction-theoretic proof of the known level $-2$ result for $D_\\ell$, and obtain a rank-reduction proof of the maximal-ideal theorem for the collapsing family $V^{2-2r}(D_{2r})$. Consequently, every candidate quotient appearing in Arakawa--Moreau Conjecture 1 is the corresponding simple affine vertex algebra.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.25249",
  "author_total": 1,
  "authors": [
    {
      "name": "Sihai Jin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6d5fjnr1xxmfv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.25249",
  "fulltext_url": null,
  "id": "6d5fjnr1xxmfv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.25249",
  "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": "W7171675469",
  "pdf_url": "https://arxiv.org/pdf/2607.25249",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6d5fjnr1xxmfv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:57Z",
      "native_id": "2607.25249",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.25249"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Completing the Arakawa--Moreau Conjecture on Maximal Ideals of Affine Vertex Algebras",
  "title_text": "Completing the Arakawa--Moreau Conjecture on Maximal Ideals of Affine Vertex Algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:57Z",
  "url": "https://research.draconitic.com/paper/6d5fjnr1xxmfv",
  "venue": "arXiv",
  "versions": []
}