{
  "id": "1704.07903",
  "version": "v1",
  "published": "2017-04-25T21:01:31.000Z",
  "updated": "2017-04-25T21:01:31.000Z",
  "title": "The centralizer of $K$ in $U(\\mathfrak{g}) \\otimes C(\\mathfrak{p})$ for the group $SO_e(4,1)$",
  "authors": [
    "Ana Prlić"
  ],
  "comment": "14 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $G$ be the Lie group $SO_e(4,1)$, with maximal compact subgroup $K = S(O(4) \\times O(1))_e\\cong SO(4)$. Let $\\mathfrak{g}=\\mathfrak{so}(5,\\mathbb{C})$ be the complexification of the Lie algebra $\\mathfrak{g}_0 = \\mathfrak{so}(4,1)$ of $G$, and let $U(\\mathfrak{g})$ be the universal enveloping algebra of $\\mathfrak{g}$. Let $\\mathfrak{g} = \\mathfrak{k} \\oplus \\mathfrak{p}$ be the Cartan decomposition of $\\mathfrak{g}$, and $C(\\mathfrak{p})$ the Clifford algebra of $\\mathfrak{p}$ with respect to the trace form $B(X, Y) = \\text{tr}(XY)$ on $\\mathfrak{p}$. In this paper we give explicit generators of the algebra $(U(\\mathfrak{g}) \\otimes C(\\mathfrak{p}))^{K}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-25T21:01:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "centralizer",
      "maximal compact subgroup",
      "explicit generators",
      "universal enveloping algebra",
      "trace form"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}