{
  "id": "1111.1295",
  "version": "v1",
  "published": "2011-11-05T10:35:44.000Z",
  "updated": "2011-11-05T10:35:44.000Z",
  "title": "Ito-Wiener chaos and the Hodge decomposition on an abstract Wiener space",
  "authors": [
    "Yuxin Yang"
  ],
  "journal": "Infinite Dimensional Analysis, Quantum Probability and Related Topics, Vol. 16, No. 1 (2013)",
  "doi": "10.1142/S0219025713500082",
  "categories": [
    "math.PR",
    "math.GN",
    "math.RT"
  ],
  "abstract": "Using the structure of the Boson-Fermion Fock space and an argument taken from [2], we give a new proof of the triviality of the $L^2$ cohomology groups on an abstract Wiener space, alternative to that given by Shigekawa [9]. We apply some representation theory of the symmetric group to characterise the spaces of exact and co-exact forms in their Boson-Fermion Fock space representation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-11-05T10:35:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58A14",
      "58A12",
      "58B05",
      "20C35",
      "60H30"
    ],
    "keywords": [
      "abstract wiener space",
      "hodge decomposition",
      "ito-wiener chaos",
      "boson-fermion fock space representation",
      "argument taken"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.1295Y"
    }
  }
}