{
  "id": "math-ph/0512047",
  "version": "v1",
  "published": "2005-12-14T21:05:17.000Z",
  "updated": "2005-12-14T21:05:17.000Z",
  "title": "From Orbital Varieties to Alternating Sign Matrices",
  "authors": [
    "P. Di Francesco",
    "P. Zinn-Justin"
  ],
  "categories": [
    "math-ph",
    "math.CO",
    "math.MP"
  ],
  "abstract": "We study a one-parameter family of vector-valued polynomials associated to each simple Lie algebra. When this parameter $q$ equals -1 one recovers Joseph polynomials, whereas at $q$ cubic root of unity one obtains ground state eigenvectors of some integrable models with boundary conditions depending on the Lie algebra; in particular, we find that the sum of its entries is related to numbers of Alternating Sign Matrices and/or Plane Partitions in various symmetry classes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-12-14T21:05:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "alternating sign matrices",
      "orbital varieties",
      "simple lie algebra",
      "ground state eigenvectors",
      "cubic root"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.ph..12047D"
    }
  }
}