{
  "abstract": "The symmetric Macdonald polynomial at peculiar values of parameter $t=q^{-m}$, $m\\in\\mathbb{Z}_{\\ge 0}$ is naturally split into non-symmetric parts, which are the (quasi)polynomial Baker-Akhiezer (BA) functions. One may think this is due to symmetricity, and one just picks up this way non-symmetric parts already containing all the information. However, we demonstrate that, in the case of {\\bf non-symmetric} Macdonald polynomials, it still works, though each single BA function splits into $N!$ distinct (quasi)polynomial BA functions. The sum of these functions gives rise to the universal solution of the eigenstate problem for the Cherednik Hamiltonians. Extending to arbitrary values of $t$ is also immediate giving rise to counterparts of the Noumi-Shiraishi power series. Altogether, this power series and its reductions to non-symmetric Macdonald polynomials and to BA functions form a non-symmetric triad. There are $N!$ different branches of the non-symmetric triad, each branch being split into $N!$ distinct triads, and of these $(N!)^2$ triads $N!(N-1)!$ are independent. We describe in detail the simplest $N=2$ case.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01517",
  "author_total": 3,
  "authors": [
    {
      "name": "A. Mironov"
    },
    {
      "name": "A. Morozov"
    },
    {
      "name": "A. Popolitov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9j0qfkgdpn5mb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01517",
  "fulltext_url": null,
  "id": "9j0qfkgdpn5mb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01517",
  "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"
    ],
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      "openalex",
      "2608|Algebraic structures and combinatorial models"
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  "openalex": "W7206197782",
  "pdf_url": "https://arxiv.org/pdf/2609.01517",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9j0qfkgdpn5mb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:00Z",
      "native_id": "2609.01517",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01517"
    }
  ],
  "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": "Non-symmetric triads and Baker-Akhiezer functions",
  "title_text": "Non-symmetric triads and Baker-Akhiezer functions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/9j0qfkgdpn5mb",
  "venue": "arXiv",
  "versions": []
}