{
  "id": "math/0610285",
  "version": "v2",
  "published": "2006-10-09T13:39:27.000Z",
  "updated": "2007-08-26T06:10:22.000Z",
  "title": "Representations of Lie groups and random matrices",
  "authors": [
    "Benoit Collins",
    "Piotr Sniady"
  ],
  "journal": "Trans. Amer. Math. Soc. 361 (2009), no. 6, 3269--3287",
  "doi": "10.1090/S0002-9947-09-04624-8",
  "categories": [
    "math.PR",
    "math.RT"
  ],
  "abstract": "We study the asymptotics of representations of a fixed compact Lie group. We prove that the limit behavior of a sequence of such representations can be described in terms of certain random matrices; in particular operations on representations (for example: tensor product, restriction to a subgroup) correspond to some natural operations on random matrices (respectively: sum of independent random matrices, taking the corners of a random matrix). Our method of proof is to treat the canonical block matrix associated to a representation as a random matrix with non-commutative entries.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-08-26T06:10:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E46",
      "46L53",
      "15A52"
    ],
    "keywords": [
      "representation",
      "random matrix",
      "fixed compact lie group",
      "independent random matrices",
      "natural operations"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Trans. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....10285C"
    }
  }
}