{
  "abstract": "We have previously, for a given positive integer $n$, explicitly characterized by certain linear inequalities the $\\mathfrak{k}$-highest weight tableaux of shape length $2n$ or $2n-1$ produced by $1$-$0$-slack recording tableaux in the quantum Littlewood-Richardson (LR) rule. We now extend that characterization for lower shape lengths. Then using the composition of promotion operators defining the Naito-Suzuki-Watanabe bijection between $\\mathfrak{k}$-highest weight tableaux and $\\widehat{\\mathfrak{g}}$-dominant tableaux, we also explicitly characterize by certain linear inequalities the corresponding $\\widehat{\\mathfrak{g}}$-dominant tableaux when the shape length is $2n$ or $2n-1$. In addition, when the given $n$ is $3$ or $ 4$ the $\\mathfrak{k}$-highest weight and the $\\widehat{\\mathfrak{g}}$-dominant tableaux via $1$-$0$-slack recording tableaux are characterized by linear inequalities for lower shape lengths. Since recording tableaux in the quantum Littlewood-Richardson rule are in natural bijection with Littlewood-Richardson-Sundaram (LRS) tableaux, we relate our results on the inverse quantum LR rule with other two bijections for the Naito-Sagaki conjecture and establish bijections between $\\mathfrak{k}$-highest weight tableaux, $\\widehat{\\mathfrak{g}}$-dominant tableaux and the lattice points in a (disjoint) union of flagged hive polytopes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.16800",
  "author_total": 1,
  "authors": [
    {
      "name": "Olga Azenhas"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7s95y5yf75d0a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.16800",
  "fulltext_url": null,
  "id": "7s95y5yf75d0a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.16800",
  "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"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7203662386",
  "pdf_url": "https://arxiv.org/pdf/2608.16800",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7s95y5yf75d0a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2608.16800",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.16800"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Characterization of $\\mathfrak{k}$-highest weight and $\\widehat{\\mathfrak{g}}$-dominant tableaux via $1$-$0$-slack recording tableaux in the quantum Littlewood-Richardson rule and lattice points in flagged hive polytopes",
  "title_text": "Characterization of k-highest weight and ĝ-dominant tableaux via $1−0$-slack recording tableaux in the quantum Littlewood-Richardson rule and lattice points in flagged hive polytopes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/7s95y5yf75d0a",
  "venue": "arXiv",
  "versions": []
}