{
  "id": "1207.2446",
  "version": "v1",
  "published": "2012-07-10T19:29:42.000Z",
  "updated": "2012-07-10T19:29:42.000Z",
  "title": "Macdonald Polynomials and BGG reciprocity for current algebras",
  "authors": [
    "Matthew Bennett",
    "Arkady Berenstein",
    "Vyjayanthi Chari",
    "Anton Khoroshkin",
    "Sergey Loktev"
  ],
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "We study the category of graded representations with finite--dimensional graded pieces for the current algebra associated to a simple Lie algebra. This category has many similarities with the category $\\cal O$ of modules for $\\lie g$ and in this paper, we use the combinatorics of Macdonald polynomials to prove an analogue of the famous BGG duality in the case of $\\lie{sl}_{n+1}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-07-10T19:29:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "current algebra",
      "macdonald polynomials",
      "bgg reciprocity",
      "simple lie algebra",
      "finite-dimensional graded pieces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.2446B"
    }
  }
}