{
  "id": "math/0601607",
  "version": "v1",
  "published": "2006-01-25T11:01:39.000Z",
  "updated": "2006-01-25T11:01:39.000Z",
  "title": "Schur-Weyl reciprocity for the q-analogue of the alternating group",
  "authors": [
    "Hideo Mitsuhashi"
  ],
  "comment": "24 pages",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "We establish Schur-Weyl reciprocity for the q-analogue of the alternating group. We analyze the sign q-permutation representation of the Hecke algebra on the tensor product of the super vector space V in detail, and examine its restriction to the q-analogue of the alternating group. In consequence, we find out that if the dimensions of even part and odd part of V are same, then the centralizer of the q-analogue of the alternating group is a Z_2-crossed product of the centralizer of the Hecke algebra and obtain Schur-Weyl reciprocity between them. Though the structure of the centralizer is more complicated for the general case, we obtained some results about the case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-01-25T11:01:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "alternating group",
      "q-analogue",
      "hecke algebra",
      "centralizer",
      "sign q-permutation representation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......1607M"
    }
  }
}