{
  "id": "0705.4142",
  "version": "v1",
  "published": "2007-05-29T05:02:19.000Z",
  "updated": "2007-05-29T05:02:19.000Z",
  "title": "Specht modules and semisimplicity criteria for Brauer and Birman--Murakami--Wenzl Algebras",
  "authors": [
    "John Enyang"
  ],
  "doi": "10.1007/s10801-007-0058-3",
  "categories": [
    "math.RT"
  ],
  "abstract": "A construction of bases for cell modules of the Birman--Murakami--Wenzl (or B--M--W) algebra $B_n(q,r)$ by lifting bases for cell modules of $B_{n-1}(q,r)$ is given. By iterating this procedure, we produce cellular bases for B--M--W algebras on which a large abelian subalgebra, generated by elements which generalise the Jucys--Murphy elements from the representation theory of the Iwahori--Hecke algebra of the symmetric group, acts triangularly. The triangular action of this abelian subalgebra is used to provide explicit criteria, in terms of the defining parameters $q$ and $r$, for B--M--W algebras to be semisimple. The aforementioned constructions provide generalisations, to the algebras under consideration here, of certain results from the Specht module theory of the Iwahori--Hecke algebra of the symmetric group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-05-29T05:02:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "birman-murakami-wenzl algebras",
      "semisimplicity criteria",
      "b-m-w algebras",
      "iwahori-hecke algebra",
      "symmetric group"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0705.4142E"
    }
  }
}