{
  "abstract": "We describe two-parametric Littlewood identities for inhomogeneous stable spin Hall-Littlewood and inhomogeneous spin $q$-Whittaker symmetric functions. These identities generalize the Littlewood identity found by Warnaar (2006) for the ordinary Hall-Littlewood polynomials. However, instead of Rogers-Szegö coefficients used by Warnaar, coefficients in our identities are given by products of Al-Salam-Chihara polynomials. Our proof relies on integrable lattice models. A key step includes three new solutions to the reflection and boundary equations for the fully fused six-vertex model. To find these solutions we use isomorphisms between tensor products of evaluation $U_q(L\\mathfrak{sl}_2)$-modules, as well as covectors stable under a $q$-Onsager coideal subalgebra.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.36644",
  "author_total": 2,
  "authors": [
    {
      "name": "Svetlana Gavrilova"
    },
    {
      "name": "Sergei Korotkikh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/343sy1evcp21s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.36644",
  "fulltext_url": null,
  "id": "343sy1evcp21s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.36644",
  "language": null,
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  "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-ph"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.MP"
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    [
      "arxiv",
      "math.QA"
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      "openalex",
      "2608|Algebraic structures and combinatorial models"
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  "openalex": "W7224097397",
  "pdf_url": "https://arxiv.org/pdf/2610.36644",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/343sy1evcp21s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:50Z",
      "native_id": "2610.36644",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.36644"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Reflection equations and Littlewood identities for spin Hall-Littlewood and $q$-Whittaker functions",
  "title_text": "Reflection equations and Littlewood identities for spin Hall-Littlewood and q-Whittaker functions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/343sy1evcp21s",
  "venue": "arXiv",
  "versions": []
}