{
  "id": "2407.13127",
  "version": "v1",
  "published": "2024-07-18T03:35:03.000Z",
  "updated": "2024-07-18T03:35:03.000Z",
  "title": "PBW bases for $\\imath$quantum groups",
  "authors": [
    "Ming Lu",
    "Ruiqi Yang",
    "Weinan Zhang"
  ],
  "comment": "33 pages; comments are welcome",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "We establish PBW type bases for $\\imath$quantum groups of arbitrary finite type, using the relative braid group symmetries. Explicit formulas for root vectors are provided for $\\imath$quantum groups of each rank 1 type. We show that our PBW type bases give rise to integral bases for the modified $\\imath$quantum groups. The leading terms of our bases can be identified with the usual PBW bases in the theory of quantum groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-18T03:35:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B37"
    ],
    "keywords": [
      "quantum groups",
      "establish pbw type bases",
      "arbitrary finite type",
      "relative braid group symmetries",
      "usual pbw bases"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}