{
  "id": "math/0501353",
  "version": "v1",
  "published": "2005-01-21T19:17:25.000Z",
  "updated": "2005-01-21T19:17:25.000Z",
  "title": "On the X=M=K Conjecture",
  "authors": [
    "Mark Shimozono"
  ],
  "comment": "requires the provided style file rcyoungtab.sty",
  "categories": [
    "math.CO",
    "math.QA"
  ],
  "abstract": "In the large rank limit, for any nonexceptional affine algebra, the graded branching multiplicities known as one-dimensional sums, are conjectured to have a simple relationship with those of type A, which are known as generalized Kostka polynomials. This is called the X=M=K conjecture. It is proved for tensor products of the symmetric power Kirillov-Reshetikhin modules for all nonexceptional affine algebras except those whose Dynkin diagrams are isomorphic to that of untwisted affine type D near the zero node. Combined with results of Lecouvey, this realizes the above one-dimensional sums of affine type C, as affine Kazhdan-Lusztig polynomials (and conjecturally for type D).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-01-21T19:17:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B37",
      "81R10",
      "81R50",
      "82B23",
      "05A30"
    ],
    "keywords": [
      "conjecture",
      "nonexceptional affine algebra",
      "symmetric power kirillov-reshetikhin modules",
      "one-dimensional sums",
      "large rank limit"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 695574,
      "adsabs": "2005math......1353S"
    }
  }
}