{
  "abstract": "We give a unified account of the five families of Khovanov arc algebras $K_n^m$, $K_n^{-\\infty}$, $K_n^{+\\infty}$, $K_n^\\infty$ and $K_\\infty^\\infty$ in the framework of level-two tensor product categorifications, making explicit a perspective familiar to specialists. Our main application is a proof of the Jung--Kim conjecture: over an algebraically closed field of characteristic zero, the centre of every walled Brauer algebra is generated by supersymmetric polynomials in its Jucys--Murphy elements. We also give a homogeneous basis of the centre in terms of arc diagrams, for the grading induced by $K_\\infty^\\infty$. The proof combines a calculation of the arc-algebra centre with an explicit comparison of central actions under the Brundan--Stroppel Morita equivalence and Brundan-Kleshchev isomorphism. Along the way, we explain the relation between $K_n^{-\\infty}$ and classical super duality, and identify $K_n^{-\\infty}$ and $K_n^{+\\infty}$ as Ringel duals. We also revisit mixed Schur--Weyl duality for general linear Lie superalgebras within the same framework.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21576",
  "author_total": 1,
  "authors": [
    {
      "name": "Shunsuke Hirota"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9ahbjbrhvw872.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21576",
  "fulltext_url": null,
  "id": "9ahbjbrhvw872",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21576",
  "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.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7222425246",
  "pdf_url": "https://arxiv.org/pdf/2610.21576",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9ahbjbrhvw872.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.21576",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21576"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A Proof of the Jung-Kim Conjecture on the Centers of Walled Brauer Algebras",
  "title_text": "A Proof of the Jung-Kim Conjecture on the Centers of Walled Brauer Algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/9ahbjbrhvw872",
  "venue": "arXiv",
  "versions": []
}