{
  "abstract": "We introduce and study trigonometric weight functions of type $B$ and type $C$ arising from integrable lattice models. These functions give $q$-deformations of the factorial $K$-theoretic Schur $P$- and $Q$-functions of Ikeda and Naruse, with the $P$-functions specialized to the type $B$ case. We realize them as specializations of partition functions of a six-vertex model with triangular boundary conditions and derive their algebraic properties using the Yang-Baxter equation and properties of the $R$- and $K$-matrices. We introduce normalized weight functions and establish diagonal evaluation formulas, divisibility properties, and bounds on Newton polytopes analogous to those in type $A$, together with recursive relations and stability. We further derive branching formulas relating these functions to type $A$ weight functions, and prove equal-cardinality orthogonality and all-cardinality biorthogonality relations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15344",
  "author_total": 1,
  "authors": [
    {
      "name": "Kohei Motegi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8mb4hc4jfd54y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15344",
  "fulltext_url": null,
  "id": "8mb4hc4jfd54y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15344",
  "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-ph"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.QA"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7221762420",
  "pdf_url": "https://arxiv.org/pdf/2610.15344",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8mb4hc4jfd54y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:06Z",
      "native_id": "2610.15344",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15344"
    }
  ],
  "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": "Type $B$- and $C$- trigonometric weight functions",
  "title_text": "Type B- and C- trigonometric weight functions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/8mb4hc4jfd54y",
  "venue": "arXiv",
  "versions": []
}