{
  "id": "2204.12444",
  "version": "v1",
  "published": "2022-04-26T17:00:51.000Z",
  "updated": "2022-04-26T17:00:51.000Z",
  "title": "K-invariant Hilbert Modules and Singular Vector Bundles on Bounded Symmetric Domains",
  "authors": [
    "Harald Upmeier"
  ],
  "comment": "31 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We show that the \"eigenbundle\" (localization bundle) of certain Hilbert modules over bounded symmetric domains of rank r is a \"singular\" vector bundle (linearly fibrered complex analytic space) which decomposes as a stratified sum of homogeneous vector bundles along a canonical stratification of length r+1. The fibres are realized in terms of representation theory on the normal space of the strata.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-26T17:00:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32M15",
      "46E22",
      "14M12",
      "17C36",
      "47B35"
    ],
    "keywords": [
      "bounded symmetric domains",
      "singular vector bundles",
      "k-invariant hilbert modules",
      "linearly fibrered complex analytic space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}