{
  "abstract": "Symmetric Macdonald polynomials of $N$ variables provide eigenfunctions of the $N$-body trigonometric Ruijsenaars-Schneider integrable system at particular eigenvalues. In order to construct eigenfunctions with arbitrary eigenvalues, M. Noumi and J. Shiraishi used a recursion in $N$ (branching rule) for the symmetric Macdonald polynomials and analytically continued them. This generated a power series, which is a part of triad (universal solution). In the present paper, we demonstrate that a similar procedure is available for another integrable system, $N$-body Cherednik integrable system inspired by the DAHA of type $A$, which has non-symmetric Macdonald polynomials as its polynomial eigenfunctions. However, in this system, the generic eigenfunction is more complicated: it is not just a simple power series as in the Noumi-Shiraishi case, but has an involved structure with $N!$ branches, each of them being a sum over the Weyl chambers of power series of the Noumi-Shiraishi type. As an illustration, we also provide explicit formulas for particular cases.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Phys.Lett. B881 (2026) 140902",
  "arxiv": "2607.09203",
  "author_total": 3,
  "authors": [
    {
      "name": "A. Mironov"
    },
    {
      "name": "A. Morozov"
    },
    {
      "name": "A. Popolitov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c1wtr7b7k51v5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.09203",
  "fulltext_url": null,
  "id": "c1wtr7b7k51v5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.09203",
  "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"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.QA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2607.09203",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c1wtr7b7k51v5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:48Z",
      "native_id": "2607.09203",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.09203"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Cherednik integrable system: eigenfunctions at generic eigenvalues",
  "title_text": "Cherednik integrable system: eigenfunctions at generic eigenvalues",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:57Z",
  "url": "https://research.draconitic.com/paper/c1wtr7b7k51v5",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1016/j.physletb.2026.140902",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}