{
  "abstract": "For general central charge, we give a combinatorial formula and a geometric realization of the formal expansion of the rank-one Virasoro irregular conformal block of type $(0,0,1)$ at its irregular singular point. We realize the normalized block as a coefficientwise matrix element on the localized equivariant Hilbert--Fock space associated with Hilbert schemes of points on $\\mathbb C^2$. At $c=1$, we prove the author's conjecture and express the parameter-independent coefficients in terms of skew-tableau numbers and Littlewood--Richardson coefficients, establishing their nonnegativity and integrality. The proof combines sectorial asymptotics of screening integrals with Laguerre--Jack evaluations. We express the screening kernel using the flow of a degree-raising differential operator and compute the Jack coefficients of its exponential from the one-box Pieri rule and the shifted Jack coefficient formula of Okounkov and Olshanski.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39786",
  "author_total": 1,
  "authors": [
    {
      "name": "Hajime Nagoya"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ex7kktszd0fh3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39786",
  "fulltext_url": null,
  "id": "ex7kktszd0fh3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39786",
  "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-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39786",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ex7kktszd0fh3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:23Z",
      "native_id": "2610.39786",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39786"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "A Combinatorial Formula and a Hilbert Scheme Realization of a Rank-One Virasoro Irregular Conformal Block",
  "title_text": "A Combinatorial Formula and a Hilbert Scheme Realization of a Rank-One Virasoro Irregular Conformal Block",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/ex7kktszd0fh3",
  "venue": "arXiv",
  "versions": []
}