{
  "id": "2408.01213",
  "version": "v1",
  "published": "2024-08-02T11:57:26.000Z",
  "updated": "2024-08-02T11:57:26.000Z",
  "title": "Differential symmetry breaking operators from a line bundle to a vector bundle over real projective spaces",
  "authors": [
    "Toshihisa Kubo"
  ],
  "comment": "52 pages",
  "categories": [
    "math.RT",
    "math.DG"
  ],
  "abstract": "In this paper we classify and construct differential symmetry breaking operators $\\mathbb{D}$ from a line bundle over the real projective space $\\mathbb{R}\\mathbb{P}^n$ to a vector bundle over $\\mathbb{R}\\mathbb{P}^{n-1}$. We further determine the factorization identities of $\\mathbb{D}$ and the branching laws of the corresponding generalized Verma modules of $\\mathfrak{sl}(n+1,\\mathbb{C})$. By utilizing the factorization identities, the $SL(n,\\mathbb{R})$-representations realized on the image $\\text{Im}(\\mathbb{D})$ are also investigated.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-02T11:57:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E46",
      "17B10"
    ],
    "keywords": [
      "real projective space",
      "line bundle",
      "vector bundle",
      "factorization identities",
      "construct differential symmetry breaking operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 52,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}