{
  "id": "math/0605166",
  "version": "v1",
  "published": "2006-05-06T15:00:38.000Z",
  "updated": "2006-05-06T15:00:38.000Z",
  "title": "Induced Representations of Infinite Symmetric Group",
  "authors": [
    "N. V. Tsilevich",
    "A. M. Vershik"
  ],
  "comment": "25 pp., Ref.23",
  "categories": [
    "math.RT",
    "math.OA"
  ],
  "abstract": "We study the representations of the infinite symmetric group induced from the identity representations of Young subgroups. It turns out that such induced representations can be either of type~I or of type~II. Each Young subgroup corresponds to a partition of the set of positive integers; depending on the sizes of blocks of this partition, we divide Young subgroups into two classes: large and small subgroups. The first class gives representations of type I, in particular, irreducible representations. The most part of Young subgroups of the second class give representations of type~II and, in particular, von Neumann factors of type II. We present a number of various examples. The main problem is to find the so-called {it spectral measure of the induced representation.} The complete solution of this problem is given for two-block Young subgroups and subgroups with infinitely many singletons and finitely many finite blocks of length greater than one.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-05-06T15:00:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C32",
      "43A65",
      "43A40"
    ],
    "keywords": [
      "infinite symmetric group",
      "induced representation",
      "young subgroup corresponds",
      "two-block young subgroups",
      "divide young subgroups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......5166T"
    }
  }
}