{
  "id": "1101.2456",
  "version": "v3",
  "published": "2011-01-12T21:12:55.000Z",
  "updated": "2012-08-29T20:36:36.000Z",
  "title": "Polynomial representations and categorifications of Fock Space",
  "authors": [
    "Jiuzu Hong",
    "Oded Yacobi"
  ],
  "comment": "32 pages, to appear in Algebras and Representation Theory",
  "categories": [
    "math.RT",
    "math.CT"
  ],
  "abstract": "The rings of symmetric polynomials form an inverse system whose limit, the ring of symmetric functions, is the model for the bosonic Fock space representation of the affine Lie algebra. We categorify this construction by considering an inverse limit of categories of polynomial representation of general linear groups. We show that this limit naturally carries an action of the affine Lie algebra (in the sense of Rouquier), thereby obtaining a famiy of categorifications of the bosonic Fock space representation.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-08-29T20:36:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18D05",
      "18F30",
      "20C20",
      "20C30"
    ],
    "keywords": [
      "polynomial representation",
      "bosonic fock space representation",
      "affine lie algebra",
      "categorifications",
      "symmetric polynomials form"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1101.2456H"
    }
  }
}