{
  "id": "0909.2442",
  "version": "v2",
  "published": "2009-09-14T00:37:59.000Z",
  "updated": "2010-01-19T00:35:32.000Z",
  "title": "Affine structures and a tableau model for E_6 crystals",
  "authors": [
    "Brant Jones",
    "Anne Schilling"
  ],
  "comment": "28 pages",
  "journal": "J. Algebra 324 (2010) 2512-2542",
  "doi": "10.1016/j.jalgebra.2010.07.041",
  "categories": [
    "math.CO",
    "math.QA"
  ],
  "abstract": "We provide the unique affine crystal structure for type E_6^{(1)} Kirillov-Reshetikhin crystals corresponding to the multiples of fundamental weights s Lambda_1, s Lambda_2, and s Lambda_6 for all s \\geq 1 (in Bourbaki's labeling of the Dynkin nodes, where 2 is the adjoint node). Our methods introduce a generalized tableaux model for classical highest weight crystals of type E and use the order three automorphism of the affine E_6^{(1)} Dynkin diagram. In addition, we provide a conjecture for the affine crystal structure of type E_7^{(1)} Kirillov-Reshetikhin crystals corresponding to the adjoint node.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-01-19T00:35:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81R50",
      "81R10",
      "17B37",
      "05E99"
    ],
    "keywords": [
      "tableau model",
      "affine structures",
      "adjoint node",
      "unique affine crystal structure",
      "kirillov-reshetikhin crystals corresponding"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0909.2442J"
    }
  }
}