{
  "id": "1806.11155",
  "version": "v1",
  "published": "2018-06-28T19:38:06.000Z",
  "updated": "2018-06-28T19:38:06.000Z",
  "title": "The Harish-Chandra integral",
  "authors": [
    "Colin McSwiggen"
  ],
  "comment": "29 pages",
  "categories": [
    "math-ph",
    "math.MP",
    "math.RT"
  ],
  "abstract": "This paper introduces Harish-Chandra's integral formula for compact, connected, semisimple Lie groups. It is intended for mathematicians and physicists who are familiar with the basics of Lie groups and Lie algebras but who may not be specialists in representation theory. I present Harish-Chandra's proof of the formula in contemporary language, work out the integrals for all compact classical groups in detail, and show how to generalize the formula to compute similar integrals over arbitrary compact Lie groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-28T19:38:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22-02",
      "43A77",
      "15B52"
    ],
    "keywords": [
      "harish-chandra integral",
      "arbitrary compact lie groups",
      "harish-chandras integral formula",
      "semisimple lie groups",
      "contemporary language"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}