{
  "abstract": "Cyclotomic Brauer or cyclotomic Nazarov--Wenzl algebras arise in higher Schur--Weyl dualities involving parabolic categories $\\mathcal O$ for Lie algebras of types $B,C$ and $D$. Their connection with Kac--Moody-type categorification is substantially less developed than the corresponding type $A$ theory for cyclotomic Hecke algebras. We construct a categorical bridge between affine Brauer-type representation theory and the half-integral quasi-split type $\\operatorname{AIII}$ $\\imath$-Kac--Moody $2$-category of Bao--Shan--Wang--Webster. More precisely, an action of the affine Brauer category on a locally Schurian category, with dot spectrum exactly $\\frac{1}{2}+\\mathbb Z$, determines a generalized nilpotent $2$-representation of the even component $\\mathfrak U^{\\imath}_{+}$. Conversely, every nilpotent $2$-subrepresentation of an ambient locally Schurian $2$-representation of $\\mathfrak U^{\\imath}_{+}$ carries a compatible affine Brauer action whose dot spectrum is contained in $\\frac{1}{2}+\\mathbb Z$. Applying these constructions to cyclotomic quotients, we prove that the locally unital algebra attached to a $\\mathbf u$-admissible cyclotomic Brauer category is isomorphic to the locally unital algebra attached to the corresponding cyclotomic quotient of the principal $2$-representation of $\\mathfrak U^{\\imath}_{+}$. Consequently, the associated cyclotomic Brauer (or cyclotomic Nazarov--Wenzl) algebras acquire natural $\\mathbb Z$-gradings. To our knowledge, this is the first such categorical realization of $\\mathbf u$-admissible half-integral cyclotomic Brauer algebras by means of an $\\imath$-Kac--Moody $2$-category. It provides the categorical and graded framework toward a Brauer-type extension of the Brundan--Kleshchev--Ariki theory in which coideal algebras and $\\imath$-canonical bases are expected to replace ordinary quantum groups and canonical bases.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07018",
  "author_total": 3,
  "authors": [
    {
      "name": "Mengmeng Gao"
    },
    {
      "name": "Hebing Rui"
    },
    {
      "name": "Linliang Song"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6jn7165vjbnep.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07018",
  "fulltext_url": null,
  "id": "6jn7165vjbnep",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07018",
  "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": "W7212045459",
  "pdf_url": "https://arxiv.org/pdf/2609.07018",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6jn7165vjbnep.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2609.07018",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07018"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Affine and cyclotomic Brauer categorification via $\\imath$-Kac--Moody $2$-categories: the half-integral type $\\operatorname{AIII}$ case",
  "title_text": "Affine and cyclotomic Brauer categorification via imath-Kac--Moody $2$-categories: the half-integral type AIII case",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/6jn7165vjbnep",
  "venue": "arXiv",
  "versions": []
}