{
  "id": "1809.06290",
  "version": "v1",
  "published": "2018-09-17T15:53:58.000Z",
  "updated": "2018-09-17T15:53:58.000Z",
  "title": "Conformally covariant bi-differential operators for differential forms",
  "authors": [
    "Salem Ben Saïd",
    "Jean-Louis Clerc",
    "Khalid Koufany"
  ],
  "comment": "23 pages",
  "categories": [
    "math.RT",
    "math.DG"
  ],
  "abstract": "The classical Rankin-Cohen brackets are bi-differential operators from $C^\\infty(\\mathbb R)\\times C^\\infty(\\mathbb R)$ into $ C^\\infty(\\mathbb R)$. They are covariant for the (diagonal) action of ${\\rm SL}(2,\\mathbb R)$ through principal series representations. We construct generalizations of these operators, replacing $\\mathbb R$ by $\\mathbb R^n,$ the group ${\\rm SL}(2,\\mathbb R)$ by the group ${\\rm SO}_0(1,n+1)$ viewed as the conformal group of $\\mathbb R^n,$ and functions by differential forms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-17T15:53:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "43A85",
      "58J70",
      "22E46",
      "58A10"
    ],
    "keywords": [
      "conformally covariant bi-differential operators",
      "differential forms",
      "principal series representations",
      "classical rankin-cohen brackets",
      "construct generalizations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}