{
  "abstract": "We introduce stable symmetric series which encode normalized conjugacy classes and their multiplication operators simultaneously for all symmetric groups. This gives a direct route from the Ivanov--Kerov algebra to shifted symmetric functions and to differential operators in $U(\\mathcal W_{1+\\infty})$. Using the Goulden--Jackson product, we extend the construction to Jack polynomials, recover shifted Jack eigenvalues and Pieri-type relations, and obtain explicit candidate operators in degrees three and four. Their real and quaternionic specializations to zonal polynomials are verified by Gaussian matrix integrals and exhaustive Wick enumeration.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.25651",
  "author_total": 1,
  "authors": [
    {
      "name": "Jean-Yves Thibon"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1s3zgqr7g9gna.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.25651",
  "fulltext_url": null,
  "id": "1s3zgqr7g9gna",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.25651",
  "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.CO"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7204459562",
  "pdf_url": "https://arxiv.org/pdf/2608.25651",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1s3zgqr7g9gna.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2608.25651",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.25651"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Stable Symmetric Series, Differential Operators, and Jack Deformations",
  "title_text": "Stable Symmetric Series, Differential Operators, and Jack Deformations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/1s3zgqr7g9gna",
  "venue": "arXiv",
  "versions": []
}