{
  "id": "math/0505064",
  "version": "v1",
  "published": "2005-05-04T00:23:54.000Z",
  "updated": "2005-05-04T00:23:54.000Z",
  "title": "Braid groups and Iwahori-Hecke algebras",
  "authors": [
    "Stephen Bigelow"
  ],
  "comment": "15 pages, 4 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "This article was submitted to a volume under preparation, with Benson Farb as the editor, on the topic of open problems in surface mapping class groups. The braid group B_n is the mapping class group of an n-times punctured disk. The Iwahori-Hecke algebra H_n is a quotient of the braid group algebra of B_n by a quadratic relation in the standard generators. We discuss how to use H_n to define the Jones polynomial of a knot or link. We also summarize the classification of the irreducible representations of H_n. We conclude with some directions for future research that would apply mapping class group techniques to questions related to H_n.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-05-04T00:23:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F36",
      "20C08",
      "57M27"
    ],
    "keywords": [
      "iwahori-hecke algebra",
      "surface mapping class groups",
      "braid group algebra",
      "apply mapping class group techniques",
      "benson farb"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......5064B"
    }
  }
}