{
  "id": "1912.09281",
  "version": "v1",
  "published": "2019-12-17T19:24:15.000Z",
  "updated": "2019-12-17T19:24:15.000Z",
  "title": "A Serre presentation for the $\\imath$quantum covering groups",
  "authors": [
    "Christopher Chung"
  ],
  "comment": "28 pages including references. arXiv admin note: text overlap with arXiv:1810.12475 by other authors",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $(\\mathbf{U}, \\mathbf{U}^\\imath)$ be a quasi-split quantum symmetric pair of Kac-Moody type. The $\\imath$quantum group $\\mathbf{U}^\\imath$ admits a Serre presentation featuring the $\\imath$-Serre relations in terms of $\\imath$-divided powers. Generalizing this result, we give a Serre presentation $ \\mathbf{U}^\\imath_\\pi $ of quantum symmetric pairs $ (\\mathbf{U}_\\pi, \\mathbf{U}^\\imath_\\pi) $ for quantum covering algebras $\\mathbf{U}_\\pi$, which have an additional parameter $ \\pi $ that specializes to the Lusztig quantum group when $ \\pi = 1 $ and quantum supergroups of anisotropic type when $ \\pi = -1 $. We give a Serre presentation for $ \\mathbf{U}^\\imath_\\pi $, introducing the $\\imath^\\pi$-Serre relations and $\\imath^\\pi$-divided powers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-17T19:24:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "serre presentation",
      "quantum covering groups",
      "serre relations",
      "quasi-split quantum symmetric pair",
      "lusztig quantum group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}