{
  "id": "0812.2059",
  "version": "v2",
  "published": "2008-12-11T20:59:30.000Z",
  "updated": "2009-04-22T12:20:29.000Z",
  "title": "The Harish-Chandra isomorphism for Clifford algebras",
  "authors": [
    "Yuri Bazlov"
  ],
  "comment": "v2: added references",
  "categories": [
    "math.RT"
  ],
  "abstract": "We study the analogue of the Harish-Chandra homomorphism where the universal enveloping algebra is replaced by the Clifford algebra, $Cl(g)$, of a semisimple Lie algebra $g$. Two main goals are achieved. First, we prove that there is a Harish-Chandra type isomorphism between the subalgebra of $g$-invariants in $Cl(g)$ and the Clifford algebra of the Cartan subalgebra of $g$. Second, the Cartan subalgebra is identified, via this isomorphism, with a graded space of the so-called primitive skew-symmetric invariants of $g$. This leads to a distinguished orthogonal basis of the Cartan subalgebra, which turns out to be induced from the Lie algebra Langlands dual to $g$ via the action of its principal three-dimensional subalgebra. This settles a conjecture of Kostant.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-04-22T12:20:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "clifford algebra",
      "harish-chandra isomorphism",
      "cartan subalgebra",
      "lie algebra langlands dual",
      "semisimple lie algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0812.2059B"
    }
  }
}