{
  "id": "1707.04876",
  "version": "v1",
  "published": "2017-07-16T13:02:05.000Z",
  "updated": "2017-07-16T13:02:05.000Z",
  "title": "Rigged configuration bijection and proof of the $X=M$ conjecture for nonexceptional affine types",
  "authors": [
    "Masato Okado",
    "Anne Schilling",
    "Travis Scrimshaw"
  ],
  "comment": "30 pages, 2 figures",
  "categories": [
    "math.CO",
    "math.QA"
  ],
  "abstract": "We establish a bijection between rigged configurations and highest weight elements of a tensor product of Kirillov-Reshetikhin crystals for all nonexceptional types. A key idea for the proof is to embed both objects into bigger sets for simply-laced types $A_n^{(1)}$ or $D_n^{(1)}$, whose bijections have already been established. As a consequence we settle the $X=M$ conjecture in full generality for nonexceptional types. Furthermore, the bijection extends to a classical crystal isomorphism and sends the combinatorial $R$-matrix to the identity map on rigged configurations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-16T13:02:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B37",
      "05A19",
      "81R50",
      "82B23"
    ],
    "keywords": [
      "nonexceptional affine types",
      "rigged configuration bijection",
      "conjecture",
      "nonexceptional types",
      "highest weight elements"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}