{
  "id": "math/0202214",
  "version": "v1",
  "published": "2002-02-21T12:18:07.000Z",
  "updated": "2002-02-21T12:18:07.000Z",
  "title": "The Lawrence--Krammer representation is unitary",
  "authors": [
    "Won Taek Song"
  ],
  "comment": "16 pages, 53 pictures",
  "categories": [
    "math.GT",
    "math.RT"
  ],
  "abstract": "We show that the Lawrence--Krammer representation is unitary. We explicitly present the non-singular matrix representing the sesquilinear pairing invariant under the action. We show that reversing the orientation of a braid is equivalent to the transposition of its Lawrence--Krammer matrix followed by a certain conjugation. As corollaries it is shown that the characteristic polynomial of the Lawrence--Krammer matrix is invariant under substitution of its variables with their inverses up to multiplication by units, and is not a complete conjugacy invariant for braids.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-02-21T12:18:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F36",
      "57M07"
    ],
    "keywords": [
      "lawrence-krammer representation",
      "lawrence-krammer matrix",
      "complete conjugacy invariant",
      "characteristic polynomial",
      "sesquilinear pairing invariant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......2214S"
    }
  }
}