{
  "id": "0806.3131",
  "version": "v2",
  "published": "2008-06-19T05:26:17.000Z",
  "updated": "2009-05-05T22:32:51.000Z",
  "title": "On the uniqueness of promotion operators on tensor products of type A crystals",
  "authors": [
    "Jason Bandlow",
    "Anne Schilling",
    "Nicolas M. Thiery"
  ],
  "comment": "31 pages; 8 figures",
  "journal": "J. Algebraic Combinatorics 31 (2010) 217-251",
  "doi": "10.1007/s10801-009-0182-3",
  "categories": [
    "math.CO",
    "math.QA"
  ],
  "abstract": "The affine Dynkin diagram of type $A_n^{(1)}$ has a cyclic symmetry. The analogue of this Dynkin diagram automorphism on the level of crystals is called a promotion operator. In this paper we show that the only irreducible type $A_n$ crystals which admit a promotion operator are the highest weight crystals indexed by rectangles. In addition we prove that on the tensor product of two type $A_n$ crystals labeled by rectangles, there is a single connected promotion operator. We conjecture this to be true for an arbitrary number of tensor factors. Our results are in agreement with Kashiwara's conjecture that all `good' affine crystals are tensor products of Kirillov-Reshetikhin crystals.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-05-05T22:32:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B37",
      "81R50",
      "05E05",
      "68R05"
    ],
    "keywords": [
      "tensor product",
      "uniqueness",
      "dynkin diagram automorphism",
      "single connected promotion operator",
      "highest weight crystals"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0806.3131B"
    }
  }
}