{
  "id": "math/0503545",
  "version": "v2",
  "published": "2005-03-24T14:17:55.000Z",
  "updated": "2005-09-28T00:16:50.000Z",
  "title": "Brauer algebras, symplectic Schur algebras and Schur-Weyl duality",
  "authors": [
    "Richard Dipper",
    "Stephen Doty",
    "Jun Hu"
  ],
  "comment": "27 pages",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "In this paper we prove Schur-Weyl duality between the symplectic group and Brauer algebra over an arbitrary infinite field $K$. We show that the natural homomorphism from the Brauer algebra $B_n(-2m)$ to the endomorphism algebra of tensor space $(K^{2m})^{\\otimes n}$ as a module over the symplectic similitude group $GSp_{2m}(K)$ (or equivalently, as a module over the symplectic group $Sp_{2m}(K)$) is always surjective. Another surjectivity, that of the natural homomorphism from the group algebra for $GSp_{2m}(K)$ to the endomorphism algebra of $(K^{2m})^{\\otimes n}$ as a module over $B_n(-2m)$, is derived as an easy consequence of S.~Oehms' results [S. Oehms, J. Algebra (1) 244 (2001), 19--44].",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-09-28T00:16:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G99"
    ],
    "keywords": [
      "symplectic schur algebras",
      "brauer algebra",
      "schur-weyl duality",
      "natural homomorphism",
      "endomorphism algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......3545D"
    }
  }
}