{
  "id": "1007.0820",
  "version": "v1",
  "published": "2010-07-06T07:11:07.000Z",
  "updated": "2010-07-06T07:11:07.000Z",
  "title": "A plactic algebra of extremal weight crystals and the Cauchy identity for Schur operators",
  "authors": [
    "Jae-Hoon Kwon"
  ],
  "comment": "22 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "We give a new bijective interpretation of the Cauchy identity for Schur operators which is a commutation relation between two formal power series with operator coefficients. We introduce a plactic algebra associated with the Kashiwara's extremal weight crystals over the Kac-Moody algebra of type $A_{+\\infty}$, and construct a Knuth type correspondence preserving the plactic relations. This bijection yields the Cauchy identity for Schur operators as a homomorphic image of its associated identity for plactic characters of extremal weight crystals, and also recovers the Sagan and Stanley's correspondence for skew tableaux as its restriction.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-07-06T07:11:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B37"
    ],
    "keywords": [
      "cauchy identity",
      "schur operators",
      "plactic algebra",
      "kashiwaras extremal weight crystals",
      "formal power series"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1007.0820K"
    }
  }
}