{
  "abstract": "Let $\\mathpzc K$ be an arbitrary commutative ring containing an invertible element $\\varepsilon$. Let ${\\mathcal H}_{\\!\\vartriangle\\!}(r)_{\\mathpzc K}$ be the extended affine Hecke algebra of type $A$ with Hecke parameter $\\varepsilon$, let $Ω_{\\mathpzc K}^{\\otimes r}$ be the affine tensor space, and let ${\\mathcal S}_{\\!\\vartriangle\\!}(n,r)_{\\mathpzc K}$ be the corresponding affine quantum Schur algebra. We first prove that the natural right action of ${\\mathcal H}_{\\!\\vartriangle\\!}(r)_{\\mathpzc K}$ on $Ω_{\\mathpzc K}^{\\otimes r}$ is always faithful. Assume further that $\\mathpzc K$ is a field of characteristic $0$ and that $\\varepsilon$ is not a root of unity. We prove that, for any $n\\geq 2$, the natural algebra homomorphism $ξ_r:{\\mathcal H}_{\\!\\vartriangle\\!}(r)_{\\mathpzc K}\\rightarrow\\operatorname{End}_{{\\mathcal S}_{\\!\\vartriangle\\!}(n,r)_{\\mathpzc K}}(Ω_{\\mathpzc K}^{\\otimes r})^{\\mathrm{op}}$ is an isomorphism. This proves Conjecture~3.8.8 of \\cite{DDF}. As an application, we prove the conjecture formulated in \\cite[5.2.4]{DDF} concerning the center of the affine quantum Schur algebra. We also prove that ${\\mathcal S}_{\\!\\vartriangle\\!}(n,r)_{\\mathpzc K}$ is left and right Noetherian whenever $\\mathpzc K$ is a Noetherian commutative ring, which verify a conjecture in \\cite[Rem. 1.7]{DY}.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19608",
  "author_total": 2,
  "authors": [
    {
      "name": "Qiang Fu"
    },
    {
      "name": "Jun Hu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dm29c1xgayz5r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19608",
  "fulltext_url": null,
  "id": "dm29c1xgayz5r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19608",
  "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.QA"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7213600576",
  "pdf_url": "https://arxiv.org/pdf/2609.19608",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dm29c1xgayz5r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.19608",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19608"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Affine quantum Schur--Weyl duality",
  "title_text": "Affine quantum Schur--Weyl duality",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/dm29c1xgayz5r",
  "venue": "arXiv",
  "versions": []
}