{
  "id": "2309.13867",
  "version": "v1",
  "published": "2023-09-25T04:31:36.000Z",
  "updated": "2023-09-25T04:31:36.000Z",
  "title": "Cellularity of KLR and weighted KLRW algebras via crystals",
  "authors": [
    "Andrew Mathas",
    "Daniel Tubbenhauer"
  ],
  "comment": "48 pages, many figures, comments welcome",
  "categories": [
    "math.RT",
    "math.CO",
    "math.RA"
  ],
  "abstract": "We prove that the weighted KLRW algebras of finite type, and their cyclotomic quotients, are cellular algebras. The cellular bases are explicitly described using crystal graphs. As a special case, this proves that the KLR algebras of finite type are cellular. As one application, we compute the graded decomposition numbers of the cyclotomic algebras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-25T04:31:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18M30",
      "20C08",
      "05E10",
      "17B10",
      "18N25"
    ],
    "keywords": [
      "weighted klrw algebras",
      "cellularity",
      "finite type",
      "cyclotomic quotients",
      "cellular algebras"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 48,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}