{
  "id": "1105.6325",
  "version": "v1",
  "published": "2011-05-31T16:02:35.000Z",
  "updated": "2011-05-31T16:02:35.000Z",
  "title": "On Characters of Inductive Limits of Symmetric Groups",
  "authors": [
    "Artem Dudko",
    "Konstantin Medynets"
  ],
  "comment": "37 pages",
  "categories": [
    "math.RT",
    "math.OA"
  ],
  "abstract": "In the paper we completely describe characters (central positive-definite functions) of simple locally finite groups that can be represented as inductive limits of (products of) symmetric groups under block diagonal embeddings. Each such group $G$ defines an infinite graph (Bratteli diagram) that encodes the embedding scheme. The group $G$ acts on the space $X$ of infinite paths of the associated Bratteli diagram by changing initial edges of paths. Assuming the finiteness of the set of ergodic measures for the system $(X,G)$, we establish that each indecomposable character $\\chi :G \\rightarrow \\mathbb C$ is uniquely defined by the formula $\\chi(g) = \\mu_1(Fix(g))^{\\alpha_1}...\\mu_k(Fix(g))^{\\alpha_k}$, where $\\mu_1,...,\\mu_k$ are $G$-ergodic measures, $Fix(g) = \\{x\\in X: gx = x\\}$, and $\\alpha_1,...,\\alpha_k\\in \\{0,1,...,\\infty\\}$. We illustrate our results on the group of rational permutations of the unit interval.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-05-31T16:02:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C32",
      "20B27",
      "37B05"
    ],
    "keywords": [
      "symmetric groups",
      "inductive limits",
      "ergodic measures",
      "block diagonal embeddings",
      "simple locally finite groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1105.6325D"
    }
  }
}