{
  "abstract": "Continuing our work on the half-integral case, we construct generalized nilpotent $2$-representations of the integral quasi-split type $\\operatorname{AIII}$ $\\imath$-Kac--Moody $2$-category from affine Brauer actions with dot spectrum exactly $\\mathbb Z$ on locally Schurian $\\mathbb C$-linear categories. Conversely, nilpotent $2$-representations on such categories yield affine Brauer actions with spectrum contained in $\\mathbb Z$. At the fixed vertex $0$, we directly define corrected generators and verify the nil-Brauer and mixed relations. For $\\mathbf u$-admissible integral parameters at arbitrary positive level, we prove an isomorphism between the locally unital algebras of the cyclotomic Brauer category and a cyclotomic quotient of the principal $2$-representation. This gives compatible $\\mathbb Z$-gradings on the category and its endomorphism algebras, providing a Brauer analogue of the graded realization of type $A$ cyclotomic Hecke algebras. Over algebraically closed fields of odd characteristic $p$, we also obtain both constructions with spectrum contained in $\\mathbb F_p$, for the mixed affine datum restricted to its spectral weight subgroup.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32589",
  "author_total": 4,
  "authors": [
    {
      "name": "Mengmeng Gao"
    },
    {
      "name": "Hebing Rui"
    },
    {
      "name": "Linliang Song"
    },
    {
      "name": "Jun Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/049rkpkzfwe4t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32589",
  "fulltext_url": null,
  "id": "049rkpkzfwe4t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.32589",
  "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": "W7223707597",
  "pdf_url": "https://arxiv.org/pdf/2610.32589",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/049rkpkzfwe4t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.32589",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32589"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Affine and cyclotomic Brauer categorification via $\\imath$-Kac--Moody $2$-categories: the integral type $\\operatorname{AIII}$ case",
  "title_text": "Affine and cyclotomic Brauer categorification via imath-Kac--Moody $2$-categories: the integral type AIII case",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/049rkpkzfwe4t",
  "venue": "arXiv",
  "versions": []
}