{
  "abstract": "For a quiver without edge loops, we construct an isomorphism from the cohomology of a Nakajima quiver variety with coefficients in an arbitrary field to the Jucys--Murphy center of the corresponding cyclotomic KLR algebra over that field. In affine type $A^{(1)}_{e-1}$, combining this with a dimension count shows that this Jucys--Murphy center coincides with the full center in characteristic $0$, when the characteristic does not divide $e$, and when the characteristic equals $e$. This follows from a geometric theorem showing that the sum of these cohomology rings is cocyclic as a module over an integral form of a loop algebra. As a consequence, we prove that the center of a cyclotomic Hecke algebra of type $G(r,1,n)$ with $q\\neq 1$ over any field is generated by symmetric polynomials in its Jucys--Murphy elements, and the same holds over any commutative domain in which $q-1$ is invertible. We also prove a generalization to the integral case of the conjecture of Krylov, Paegelow and Shlykov identifying the equivariant $K$-theory of the core of a Gieseker variety with the cocenter of the generic cyclotomic Hecke algebra, including the natural extension of this conjecture to positive characteristic.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25101",
  "author_total": 4,
  "authors": [
    {
      "name": "Jun Hu"
    },
    {
      "name": "Andrew Mathas"
    },
    {
      "name": "Lei Shi"
    },
    {
      "name": "Ben Webster"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3ztv3rc97xyt4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25101",
  "fulltext_url": null,
  "id": "3ztv3rc97xyt4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25101",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.QA"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7223037603",
  "pdf_url": "https://arxiv.org/pdf/2610.25101",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3ztv3rc97xyt4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.25101",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25101"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The center conjecture for cyclotomic Hecke algebras and cohomology of quiver varieties",
  "title_text": "The center conjecture for cyclotomic Hecke algebras and cohomology of quiver varieties",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/3ztv3rc97xyt4",
  "venue": "arXiv",
  "versions": []
}