{
  "id": "1203.6434",
  "version": "v7",
  "published": "2012-03-29T05:55:26.000Z",
  "updated": "2012-11-28T04:27:47.000Z",
  "title": "A characterization of the unitary highest weight modules by Euclidean Jordan algebras",
  "authors": [
    "Zhanqiang Bai"
  ],
  "comment": "34pages, accepted by Journal of Lie Theory",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $\\mathfrak{co}(J)$ be the conformal algebra of a simple Euclidean Jordan algebra $J$. We show that a (non-trivial) unitary highest weight $\\mathfrak{co}(J)$-module has the smallest positive Gelfand-Kirillov dimension if and only if a certain quadratic relation is satisfied in the universal enveloping algebra $U(\\mathfrak{co}(J)_{\\mathbb{C}})$. In particular, we find an quadratic element in $U(\\mathfrak{co}(J)_{\\mathbb{C}})$. A prime ideal in $U(\\mathfrak{co}(J)_{\\mathbb{C}})$ equals the Joseph ideal if and only if it contains this quadratic element.",
  "revisions": [
    {
      "version": "v7",
      "updated": "2012-11-28T04:27:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "unitary highest weight modules",
      "characterization",
      "quadratic element",
      "simple euclidean jordan algebra",
      "smallest positive gelfand-kirillov dimension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1203.6434B"
    }
  }
}