{
  "id": "1404.4222",
  "version": "v1",
  "published": "2014-04-16T12:29:47.000Z",
  "updated": "2014-04-16T12:29:47.000Z",
  "title": "On special covariants in the exterior algebra of a simple Lie algebra",
  "authors": [
    "Corrado De Concini",
    "Pierluigi Möseneder Frajria",
    "Paolo Papi",
    "Claudio Procesi"
  ],
  "comment": "Latex file, 11 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "For a simple complex Lie algebra $\\mathfrak g$ we study the space $Hom_\\mathfrak g(L,\\bigwedge \\mathfrak g)$ when $L$ is either the little adjoint representation or, in type $A_{n-1}$, the $n$-th symmetric power of the defining representation. As main result we prove that $Hom_\\mathfrak g(L,\\bigwedge \\mathfrak g)$ is a free module, of rank twice the dimension of the $0$-weight space of $L$, over the exterior algebra generated by all primitive invariants in $(\\bigwedge \\mathfrak g^*)^{\\mathfrak g}$, with the exception of the one of highest degree.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-16T12:29:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "simple lie algebra",
      "exterior algebra",
      "special covariants",
      "simple complex lie algebra",
      "th symmetric power"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.4222D"
    }
  }
}