{
  "id": "1004.3076",
  "version": "v1",
  "published": "2010-04-19T01:22:46.000Z",
  "updated": "2010-04-19T01:22:46.000Z",
  "title": "A classification of homogeneous operators in the Cowen-Douglas class",
  "authors": [
    "Adam Koranyi",
    "Gadadhar Misra"
  ],
  "comment": "18 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "An explicit construction of all the homogeneous holomorphic Hermitian vector bundles over the unit disc $\\mathbb D$ is given. It is shown that every such vector bundle is a direct sum of irreducible ones. Among these irreducible homogeneous holomorphic Hermitian vector bundles over $\\mathbb D$, the ones corresponding to operators in the Cowen-Douglas class ${\\mathrm B}_n(\\mathbb D)$ are identified. The classification of homogeneous operators in ${\\mathrm B}_n(\\mathbb D)$ is completed using an explicit realization of these operators. We also show how the homogeneous operators in ${\\mathrm B}_n(\\mathbb D)$ split into similarity classes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-04-19T01:22:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B32",
      "14F05",
      "53B35"
    ],
    "keywords": [
      "homogeneous operators",
      "cowen-douglas class",
      "homogeneous holomorphic hermitian vector bundles",
      "classification",
      "irreducible homogeneous holomorphic hermitian vector"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1004.3076K"
    }
  }
}