{
  "id": "2312.15621",
  "version": "v1",
  "published": "2023-12-25T05:56:13.000Z",
  "updated": "2023-12-25T05:56:13.000Z",
  "title": "On the intertwining differential operators for line bundles over real projective spaces",
  "authors": [
    "Toshihisa Kubo",
    "Bent Ørsted"
  ],
  "comment": "29 pages",
  "categories": [
    "math.RT",
    "math.DG"
  ],
  "abstract": "We classify and construct $SL(n,\\mathbb{R})$-intertwining differential operators $\\mathcal{D}$ for line bundles over real projective space $\\mathbb{RP}^n$ by the F-method. This generalizes a classical result of Bol for $SL(2,\\mathbb{R})$. Further, we classify the $K$-type formulas for the kernel $\\mathrm{Ker}(\\mathcal{D})$ and image $\\mathrm{Im}(\\mathcal{D})$ of $\\mathcal{D}$. The standardness of the homomorphisms $\\varphi$ corresponding to the differential operators $\\mathcal{D}$ between generalized Verma modules are also discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-25T05:56:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E46",
      "17B10"
    ],
    "keywords": [
      "real projective space",
      "intertwining differential operators",
      "line bundles",
      "type formulas",
      "generalized verma modules"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}