{
  "id": "1101.1336",
  "version": "v1",
  "published": "2011-01-07T00:42:42.000Z",
  "updated": "2011-01-07T00:42:42.000Z",
  "title": "A new fusion procedure for the Brauer algebra and evaluation homomorphisms",
  "authors": [
    "A. P. Isaev",
    "A. I. Molev",
    "O. V. Ogievetsky"
  ],
  "comment": "31 pages",
  "journal": "IMRN (2012), 2571-2606",
  "doi": "10.1093/imrn/rnr126",
  "categories": [
    "math.RT",
    "math.CO",
    "math.QA"
  ],
  "abstract": "We give a new fusion procedure for the Brauer algebra by showing that all primitive idempotents can be found by evaluating a rational function in several variables which has the form of a product of R-matrix type factors. In particular, this provides a new fusion procedure for the symmetric group involving an arbitrary parameter. The R-matrices are solutions of the Yang--Baxter equation associated with the classical Lie algebras g_N of types B, C and D. Moreover, we construct an evaluation homomorphism from a reflection equation algebra B(g_N) to U(g_N) and show that the fusion procedure provides an equivalence between natural tensor representations of B(g_N) with the corresponding evaluation modules.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-01-07T00:42:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fusion procedure",
      "brauer algebra",
      "evaluation homomorphism",
      "r-matrix type factors",
      "reflection equation algebra"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1101.1336I"
    }
  }
}