{
  "id": "1803.02679",
  "version": "v1",
  "published": "2018-03-07T14:38:11.000Z",
  "updated": "2018-03-07T14:38:11.000Z",
  "title": "Inner Product of Irreducible Finite-dimensional Representations of Classical Groups",
  "authors": [
    "Chuanzhong Li",
    "Zhisheng Liu",
    "Bao Shou"
  ],
  "comment": "19 pages, 5 figures",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this paper, we study the inner product of states corresponding to weights of irreducible finite-dimensional representations of classical groups. We propose a recursion algorithm for calculating the inner product effectively. As applications, we discuss the unitary of the representations space. We construct the norms of a special kind of states. We also determine the inner product of states in the minuscule representations. These results can be used to study the construction of the solutions to Kapustin-Witten equations basing on the fundamental solutions of Toda systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-07T14:38:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "inner product",
      "irreducible finite-dimensional representations",
      "classical groups",
      "representations space",
      "fundamental solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}