{
  "abstract": "Consider the space of $C^\\infty$-functions on the two-dimensional sphere $S^2$ and its decomposition $\\oplus\\mathcal H_m$ into a direct sum of minimal rotation-invariant spaces. We consider elements of $\\oplus\\mathcal H_m$ as functions of two variables, a nonnegative integer variable $m$ and a complex variable $u$ (a restriction of such function to a set $m=k$ is a polynomial in $u$ of degree $\\le 2k$). The group $\\mathrm{GL}\\,(3,{\\mathbb R})$ of all matrices of order 3 acts on $S^2$, so its Lie algebra acts in $C^\\infty(S^2)$ by differentiations along vector fields. We construct operators in $\\mathcal W^\\infty$ corresponding such differentiations and obtain a collection of differential-difference operators in $\\mathcal W^\\infty$. The expressions include shifts $m\\mapsto m\\pm 2$ and derivatives of order 4 in $u$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28320",
  "author_total": 1,
  "authors": [
    {
      "name": "Yury A. Neretin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cdxe6tnb1157b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28320",
  "fulltext_url": null,
  "id": "cdxe6tnb1157b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28320",
  "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-ph"
    ],
    [
      "arxiv",
      "math.CA"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7223146618",
  "pdf_url": "https://arxiv.org/pdf/2610.28320",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cdxe6tnb1157b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:04Z",
      "native_id": "2610.28320",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28320"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Spherical harmonics and infinitesimal projective transformations",
  "title_text": "Spherical harmonics and infinitesimal projective transformations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/cdxe6tnb1157b",
  "venue": "arXiv",
  "versions": []
}