{
  "id": "math/0605005",
  "version": "v1",
  "published": "2006-04-29T04:26:39.000Z",
  "updated": "2006-04-29T04:26:39.000Z",
  "title": "Rational semistandard tableaux and character formula for the Lie superalgebra $\\hat{\\frak{gl}}_{\\infty|\\infty}$",
  "authors": [
    "Jae-Hoon Kwon"
  ],
  "comment": "39pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "A new combinatorial interpretation of the Howe dual pair $(\\hat{\\frak{gl}}_{\\infty|\\infty},\\frak{gl}_n)$ acting on an infinite dimensional Fock space $\\frak{F}^n$ of level $n$ is presented. The character of a quasi-finite irreducible highest weight representation of $\\hat{\\frak{gl}}_{\\infty|\\infty}$ occurring in $\\frak{F}^n$ is realized in terms of certain bitableaux of skew shapes. We study a general combinatorics of these bitableaux, including Robinson-Schensted-Knuth correspondence and Littlewood-Richardson rule, and then its dual relation with the rational semistandard tableaux for $\\frak{gl}_n$. This result also explains other Howe dual pairs including $\\frak{gl}_n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-04-29T04:26:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10",
      "05E10"
    ],
    "keywords": [
      "rational semistandard tableaux",
      "character formula",
      "lie superalgebra",
      "howe dual pair",
      "infinite dimensional fock space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......5005K"
    }
  }
}