{
  "abstract": "This paper investigates generalized conformal modules over the Virasoro conformal algebra $Vir$, a notion originally defined by V.~Kac but largely unexplored in the literature. First, we present a twisted construction that produces new generalized conformal modules over any Lie conformal algebra from existing conformal modules. Then we give a complete classification of non-trivial generalized conformal modules over $Vir$ that are free of rank one over $\\mathbb C[\\partial]$, which in turn yields a classification of modules over the Lie algebra \\(W_1=\\bigoplus_{i\\geq -1}\\C L_i\\) of vector fields on a line that are free of rank one over $\\mathbb C[L_{-1}]$ with explicit actions expressed in terms of Bell polynomials. For arbitrary finite rank $n$, we construct a class of generalized conformal modules $V_{a,b,C(\\partial)}$ and establish a complete irreducibility criterion in terms of the differential operator $\\mathcal L=\\frac{d}{d\\partial}+C(\\partial)$ acting on $\\mathbb{C}(\\partial)^n$. In the case of $n=2$, this criterion reduces to the absence of rational solutions of a Riccati equation. Then we prove the existence of irreducible generalized conformal modules of arbitrary finite rank, revealing a striking contrast with the conformal setting. We also construct and classify a family of infinite torsion generalized conformal modules over $Vir$, which are non-trivial and irreducible under suitable conditions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18184",
  "author_total": 2,
  "authors": [
    {
      "name": "Henan Wu"
    },
    {
      "name": "Yanyong Hong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7q8p9cskz7sh2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18184",
  "fulltext_url": null,
  "id": "7q8p9cskz7sh2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18184",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7213519210",
  "pdf_url": "https://arxiv.org/pdf/2609.18184",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7q8p9cskz7sh2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.18184",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18184"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Generalized conformal modules over the Virasoro conformal algebra",
  "title_text": "Generalized conformal modules over the Virasoro conformal algebra",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/7q8p9cskz7sh2",
  "venue": "arXiv",
  "versions": []
}