{
  "id": "2001.03818",
  "version": "v1",
  "published": "2020-01-12T01:25:35.000Z",
  "updated": "2020-01-12T01:25:35.000Z",
  "title": "Serre-Lusztig relations for $\\imath${}quantum groups",
  "authors": [
    "Xinhong Chen",
    "Ming Lu",
    "Weiqiang Wang"
  ],
  "comment": "44 pages",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "Let $(\\bf U, \\bf U^\\imath)$ be a quantum symmetric pair of Kac-Moody type. The $\\imath$quantum groups $\\bf U^\\imath$ and the universal $\\imath$quantum groups $\\widetilde{\\bf U}^\\imath$ can be viewed as a generalization of quantum groups and Drinfeld doubles $\\widetilde{\\bf U}$. In this paper we formulate and establish Serre-Lusztig relations for $\\imath$quantum groups in terms of $\\imath$divided powers, which are an $\\imath$-analog of Lusztig's higher order Serre relations for quantum groups. This has applications to braid group symmetries on $\\imath$quantum groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-12T01:25:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum groups",
      "lusztigs higher order serre relations",
      "quantum symmetric pair",
      "braid group symmetries",
      "drinfeld doubles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 44,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}