{
  "abstract": "For a partition $λ$, let $G_λ^{(β)}$ be the stable $β$-Grothendieck polynomial attached to $λ$. Each homogeneous component of the $β= 1$ specialization $G_λ^{(1)}$ is Schur-positive and hence positive in the fundamental basis of quasisymmetric functions. For $m\\ge|λ|$, let $G_{λ,m}^{(1)}$ be the homogeneous degree $m$ component of $G_λ^{(1)}$. In this paper, we first give a direct proof of an expansion of $G_{λ,m}^{(1)}$ in the fundamental basis in terms of standard set-valued tableaux. We then use these tableaux as a basis to define a module of the $0$-Hecke algebra and show that the quasisymmetric characteristic of the resulting module is $G_{λ,m}^{(1)}$. We further show that this module decomposes as a direct sum of weak Bruhat interval modules.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10911",
  "author_total": 1,
  "authors": [
    {
      "name": "Young-Hun Kim"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f1gdx4n3eeby9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10911",
  "fulltext_url": null,
  "id": "f1gdx4n3eeby9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10911",
  "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",
      "math.CO"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7212225168",
  "pdf_url": "https://arxiv.org/pdf/2609.10911",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f1gdx4n3eeby9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.10911",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10911"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Weak Bruhat interval modules of the 0-Hecke algebras for stable Grothendieck polynomials",
  "title_text": "Weak Bruhat interval modules of the 0-Hecke algebras for stable Grothendieck polynomials",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/f1gdx4n3eeby9",
  "venue": "arXiv",
  "versions": []
}