{
  "id": "1403.4758",
  "version": "v1",
  "published": "2014-03-19T10:37:31.000Z",
  "updated": "2014-03-19T10:37:31.000Z",
  "title": "New homogeneous ideals for current algebras: filtrations, fusion products and Pieri rules",
  "authors": [
    "Ghislain Fourier"
  ],
  "comment": "23 pages",
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "New graded modules for the current algebra of $\\mathfrak{sl}_n$ are introduced. Relating these modules to the fusion product of simple $\\mathfrak{sl}_n$-modules and local Weyl modules of truncated current algebras shows their expected impact on several outstanding conjectures. We further generalize results on PBW filtrations of simple $\\mathfrak{sl}_n$-modules and use them to provide decomposition formulas for these new modules in important cases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-03-19T10:37:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10",
      "17B70",
      "05E10",
      "05E05"
    ],
    "keywords": [
      "fusion product",
      "pieri rules",
      "homogeneous ideals",
      "local weyl modules",
      "decomposition formulas"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.4758F"
    }
  }
}