{
  "id": "1303.3167",
  "version": "v2",
  "published": "2013-03-13T14:21:44.000Z",
  "updated": "2013-03-14T03:15:28.000Z",
  "title": "On the vector bundles associated to irreducible representations of cocompact lattices of SL(2,C)",
  "authors": [
    "Indranil Biswas",
    "Avijit Mukherjee"
  ],
  "comment": "A couple of typos corrected",
  "categories": [
    "math.DG",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this continuation of \\cite{BM}, we prove the following: Let $\\Gamma\\subset \\text{SL}(2,{\\mathbb C})$ be a cocompact lattice, and let $\\rho: \\Gamma \\rightarrow \\text{GL}(r,{\\mathbb C})$ be an irreducible representation. Then the holomorphic vector bundle $E_\\rho \\longrightarrow \\text{SL}(2,{\\mathbb C})/\\Gamma$ associated to $\\rho$ is polystable. The compact complex manifold $\\text{SL}(2,{\\mathbb C})/\\Gamma$ has natural Hermitian structures; the polystability of $E_\\rho$ is with respect to these natural Hermitian structures.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-03-14T03:15:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81T30",
      "14D21",
      "53C07"
    ],
    "keywords": [
      "vector bundles",
      "cocompact lattice",
      "irreducible representation",
      "natural hermitian structures",
      "compact complex manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1303.3167B"
    }
  }
}