{
  "id": "1810.12475",
  "version": "v1",
  "published": "2018-10-30T01:22:29.000Z",
  "updated": "2018-10-30T01:22:29.000Z",
  "title": "A Serre presentation for the $\\imath$quantum groups",
  "authors": [
    "Xinhong Chen",
    "Ming Lu",
    "Weiqiang Wang"
  ],
  "comment": "29 pages",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "Let $(\\bf U, \\bf U^\\imath)$ be a quasi-split quantum symmetric pair of arbitrary Kac-Moody type, where \"quasi-split\" means the corresponding Satake diagram contains no black node. We give a presentation of the $\\imath$quantum group $\\bf U^\\imath$ with explicit $\\imath$Serre relations. The verification of new $\\imath$Serre relations are reduced to some new q-binomial identities. Consequently, $\\bf U^\\imath$ is shown to admit a bar involution under suitable conditions on the parameters.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-30T01:22:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum group",
      "serre presentation",
      "quasi-split quantum symmetric pair",
      "serre relations",
      "corresponding satake diagram contains"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}