{
  "abstract": "The shifted Jack Littlewood-Richardson coefficients generalize the ordinary Jack coefficients and are Laurent polynomials in the Jack parameter $α$. We prove a previously conjectured congruence: coefficients indexed by triples differing by a single box move are congruent modulo the shared $α$-hook at the pivot. We also prove a shifted Macdonald analogue, with a power-of-$t$ twist, and establish that the normalized shifted Macdonald coefficients are Laurent polynomials in $q$ and $t$. The proofs combine coincidences of shifted coordinates with Laurent-preserving shift transforms, and the Macdonald input uses Knop's inversion formula and the integrality of the Bergeron-Garsia-Haiman-Tesler operators. Finally, we realize the Jack and Macdonald congruences as necessary edge conditions on Hilbert schemes of points, in equivariant cohomology and equivariant $K$-theory, respectively. In the Macdonald case a tautological determinant twist accounts for the power-of-$t$ normalization",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.17822",
  "author_total": 1,
  "authors": [
    {
      "name": "Ryan Mickler"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cdkh471gssz80.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.17822",
  "fulltext_url": null,
  "id": "cdkh471gssz80",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.17822",
  "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.CO"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7165000789",
  "pdf_url": "https://arxiv.org/pdf/2606.17822",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cdkh471gssz80.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2606.17822",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.17822"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Congruences of shifted Jack Littlewood-Richardson coefficients",
  "title_text": "Congruences of shifted Jack Littlewood-Richardson coefficients",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/cdkh471gssz80",
  "venue": "arXiv",
  "versions": []
}