{
  "abstract": "We give an explicit formula for elements $H_{2k}$ of conformal weight $2k$, $k\\ge1$, in the universal Virasoro vertex operator algebra $V$ at every central charge, such that $H_{2k}(0)H_{2l}\\in TV$ for all $k,l\\ge1$. Modulo translation, the kernel of $H_4(0)$ is generated by $[H_{2k}]$ in each positive even weight and is zero in positive odd weights. The formula uses a realization on differential polynomials by possibly infinite-order differential operators in a completion of the Weyl algebra, together with the inverse of the identity plus a nilpotent operator on each weight space. A Koszul-type exactness argument for the classical KdV flows proves conservation; uniqueness and the Jacobi identity give commutativity. The classical limit recovers the normalized Gelfand--Dickey densities. Explicit low-weight elements and exact symbolic verifications illustrate the construction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06767",
  "author_total": 1,
  "authors": [
    {
      "name": "Hongbo Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/78ep9dj3ca6x9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06767",
  "fulltext_url": null,
  "id": "78ep9dj3ca6x9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06767",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.QA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06767",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/78ep9dj3ca6x9.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.06767",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06767"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "An Explicit Construction of Commuting Quantum KdV Hamiltonians in the Universal Virasoro Vertex Algebra",
  "title_text": "An Explicit Construction of Commuting Quantum KdV Hamiltonians in the Universal Virasoro Vertex Algebra",
  "type": "preprint",
  "updated_at": "2026-11-07T18:20:08Z",
  "url": "https://research.draconitic.com/paper/78ep9dj3ca6x9",
  "venue": "arXiv",
  "versions": []
}