{
  "abstract": "In this paper we study the relations between the Hamiltonian hierarchy generated by trigonometric Cherednik-Dunkl operators and the one generated by rational Dunkl operators. We develop two nested structures relating these two hierarchies. The first nested relation reconstructs the higher rational spin Calogero-Sutherland Hamiltonians exactly from the trigonometric ones. The second nested relation reconstructs the higher trigonometric spin Calogero-Sutherland Hamiltonians as leading terms from the rational ones. In addition, we provide an explanation of the eigenvalues of the trigonometric spin Calogero-Sutherland Hamiltonians in terms of $N$-colored Young diagrams and Maya diagrams.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14330",
  "author_total": 4,
  "authors": [
    {
      "name": "Yue Li"
    },
    {
      "name": "Fan Liu"
    },
    {
      "name": "Lu-Yao Wang"
    },
    {
      "name": "Jie Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fb4ft8c8pgck9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14330",
  "fulltext_url": null,
  "id": "fb4ft8c8pgck9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14330",
  "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",
      "hep-th"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7213332842",
  "pdf_url": "https://arxiv.org/pdf/2609.14330",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fb4ft8c8pgck9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:25Z",
      "native_id": "2609.14330",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14330"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Relations between the higher Hamiltonians of the trigonometric and the rational spin Calogero-Sutherland models",
  "title_text": "Relations between the higher Hamiltonians of the trigonometric and the rational spin Calogero-Sutherland models",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:25Z",
  "url": "https://research.draconitic.com/paper/fb4ft8c8pgck9",
  "venue": "arXiv",
  "versions": []
}