{
  "id": "2506.17070",
  "version": "v1",
  "published": "2025-06-20T15:16:31.000Z",
  "updated": "2025-06-20T15:16:31.000Z",
  "title": "A diagrammatic approach to reflection functors",
  "authors": [
    "Haruto Murata"
  ],
  "comment": "Draft version. An expanded version is in preparation",
  "categories": [
    "math.RT"
  ],
  "abstract": "We construct reflection functors for quiver Hecke algebras associated with arbitrary symmetrizable Kac-Moody algebras, from a higher representation-theoretic viewpoint. These functors provide a categorification of Lusztig's braid group action on the quantum group. Similar functors were recently constructed independently by Kashiwara-Kim-Oh-Park via a different approach.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-06-20T15:16:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G42",
      "18N25",
      "20C08",
      "16T20"
    ],
    "keywords": [
      "diagrammatic approach",
      "lusztigs braid group action",
      "construct reflection functors",
      "quiver hecke algebras",
      "higher representation-theoretic viewpoint"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}