{
  "id": "1211.7091",
  "version": "v2",
  "published": "2012-11-29T21:16:05.000Z",
  "updated": "2015-02-05T17:50:40.000Z",
  "title": "Multiplication of conjugacy classes, colligations, and characteristic functions of matrix argument",
  "authors": [
    "Yury A. Neretin"
  ],
  "comment": "20pp, extended version",
  "categories": [
    "math.RT",
    "math.GR"
  ],
  "abstract": "We extend the classical construction of operator colligations and characteristic functions. Consider the group $G$ of finite block unitary matrices of size $\\alpha+\\infty+...+\\infty$ ($k$ times). Consider the subgroup $K=U(\\infty)$, which consists of block diagonal unitary matrices (with a block 1 of size $\\alpha$ and a matrix $u\\in U(\\infty)$ repeated $k$ times). It appears that there is a natural multiplication on the conjugacy classes $G//K$. We construct 'spectral data' of conjugacy classes, which visualize the multiplication and are sufficient for a reconstruction of a conjugacy class.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-11-29T21:16:05.000Z",
      "comment": "15pp",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-02-05T17:50:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E66",
      "47A48",
      "15A72",
      "16W22"
    ],
    "keywords": [
      "conjugacy classes",
      "characteristic functions",
      "matrix argument",
      "finite block unitary matrices",
      "block diagonal unitary matrices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.7091N"
    }
  }
}