{
  "id": "math/9906148",
  "version": "v4",
  "published": "1999-06-22T14:49:20.000Z",
  "updated": "2003-07-08T14:15:30.000Z",
  "title": "Mixed hook-length formula for degenerate affine Hecke algebras",
  "authors": [
    "Maxim Nazarov"
  ],
  "comment": "AmS-TeX, 12 pages, final version",
  "journal": "Lecture Notes in Math. 1815 (2003), 223-236",
  "categories": [
    "math.RT",
    "math.CO",
    "math.QA"
  ],
  "abstract": "Take the degenerate affine Hecke algebra $H_{l+m}$ corresponding to the group $GL_{l+m}$ over a $p$-adic field. Consider the $H_{l+m}$-module $W$ induced from the tensor product of the evaluation modules over the algebras $H_l$ and $H_m$. The module $W$ depends on two partitions $\\lambda$ of $l$ and $\\mu$ of $m$, and on two complex numbers $z$ and $w$. There is a canonical operator $J$ acting in $W$, it corresponds to the rational Yang $R$-matrix. The algebra $H_{l+m}$ contains the symmetric group $S_{l+m}$, and $J$ commutes with the action of $S_{l+m}$ in $W$. Under this action, $W$ decomposes into irreducible subspaces according to the Littlewood-Richardson rule. We compute the eigenvalues of $J$, corresponding to certain multiplicity-free irreducible components of $W$. In particular, we obtain a nice formula for the ratio of two eigenvalues of $J$, corresponding to the \"highest\" and \"lowest\" (multiplicity-free) irreducible components of $W$.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2003-07-08T14:15:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "degenerate affine hecke algebra",
      "mixed hook-length formula",
      "complex numbers",
      "adic field",
      "nice formula"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "AMS-TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math......6148N"
    }
  }
}