{
  "schema_version": 1,
  "problem_number": "AIM-REPRESENTATION_THEORY-0023",
  "title": "Quantum Symmetric Algebras on Multiple Standard Copies: Structure and Categorical Non-Equivalence",
  "author": {
    "name": "Alper Ferudun",
    "affiliation": "Mercury Software GmbH",
    "url": "https://github.com/AlperTheKing"
  },
  "abstract": "Let E be the standard object in the generic polynomial Hecke category over C(q), and let U be an ordinary finite-dimensional multiplicity space. We determine every homogeneous component of the Berenstein-Zwicknagl quantum symmetric algebra A = S_sigma(E tensor U): in degree n >= 2, only the one-row and one-column representations survive, with multiplicities Sym^n U and exterior^n U. We identify A as a fiber product of two diagonal algebras over its square-zero degree-one truncation. For dim U >= 2, its full category of internal polynomial right modules is not equivalent to the corresponding classical module category, even as an abstract abelian category. The obstruction intrinsically identifies two simple objects whose projective covers have a zero Hom space quantumly and a nonzero Hom space classically. The proof uses an explicit two-dimensional Hecke braid defect.",
  "result_type": "COMPLETE_NEGATIVE_ANSWER",
  "categories": [
    "math.QA",
    "math.RT"
  ],
  "keywords": [
    "quantum symmetric algebra",
    "Hecke algebra",
    "Berenstein-Zwicknagl commutor",
    "polynomial representation",
    "module category",
    "Young graph",
    "projective cover",
    "fiber product",
    "AIM-REPRESENTATION_THEORY-0023",
    "math.QA",
    "math.RT",
    "open mathematics",
    "mathematical proof"
  ],
  "manuscript_version_date": "2026-09-07",
  "publication_date": "2026-09-07",
  "publication_date_kind": "first public online release",
  "version": "1.0",
  "date_modified": "2026-09-07",
  "presentation_revision_only": false,
  "doi_archived_file_version": "1.0",
  "status": "unrefereed preprint",
  "canonical_url": "https://eulersolve.org/papers/aim-representation-theory-0023/",
  "pdf_url": "https://eulersolve.org/papers/aim-representation-theory-0023/paper.pdf?v=a1f3da138ab4",
  "doi": "10.5281/zenodo.22635788",
  "zenodo_record_url": "https://zenodo.org/records/22635788",
  "license": "https://creativecommons.org/licenses/by/4.0/",
  "scope_caveat": "Accepted complete proof in the explicit generic multiple-standard full-module category. Unrefereed; no independent/formal review or absolute priority certification. The already published package bytes are unchanged.",
  "files": {
    "paper.pdf": {
      "sha256": "a1f3da138ab402204eab706c37d07643b4469ff98e4c531bc8c607ed15654b71"
    },
    "source.zip": {
      "sha256": "f552ebc178dc1a90cec253a66e3fe7d376a52c3ab0500b46ee8406bfb7a7cb02"
    },
    "verification_report.md": {
      "sha256": "9eae9200466365d9739df8250360236651ed861f95b00ab5002f855c0914aff4"
    }
  },
  "ai_use_disclosure": "AI-assisted tools supported literature search, computation, proof auditing, and manuscript preparation. The author remains responsible for all claims and the final text."
}