{
  "id": "1207.0076",
  "version": "v1",
  "published": "2012-06-30T10:41:01.000Z",
  "updated": "2012-06-30T10:41:01.000Z",
  "title": "Induced representations of infinite-dimensional groups",
  "authors": [
    "Alexandre Kosyak"
  ],
  "categories": [
    "math.RT",
    "math.GR"
  ],
  "abstract": "The induced representation ${\\rm Ind}_H^GS$ of a locally compact group $G$ is the unitary representation of the group $G$ associated with unitary representation $S:H\\rightarrow U(V)$ of a subgroup $H$ of the group $G$. Our aim is to develop the concept of induced representations for infinite-dimensional groups. The induced representations for infinite-dimensional groups in not unique, as in the case of a locally compact groups. It depends on two completions $\\tilde H$ and $\\tilde G$ of the subgroup $H$ and the group $G$, on an extension $\\tilde S:\\tilde H\\rightarrow U(V)$ of the representation $S:H\\rightarrow U(V)$ and on a choice of the $G$-quasi-invariant measure $\\mu$ on an appropriate completion $\\tilde X=\\tilde H\\backslash \\tilde G$ of the space $H\\backslash G$. As the illustration we consider the \"nilpotent\" group $B_0^{\\mathbb Z}$ of infinite in both directions upper triangular matrices and the induced representation corresponding to the so-called generic",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-06-30T10:41:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "induced representation",
      "infinite-dimensional groups",
      "locally compact group",
      "unitary representation",
      "directions upper triangular matrices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.0076K"
    }
  }
}