{
  "id": "1511.07045",
  "version": "v1",
  "published": "2015-11-22T18:21:36.000Z",
  "updated": "2015-11-22T18:21:36.000Z",
  "title": "Conical Representations for Direct Limits of Symmetric Spaces",
  "authors": [
    "Matthew Dawson",
    "Gestur Olafsson"
  ],
  "comment": "38 pages, 2 figures, 3 tables",
  "categories": [
    "math.RT"
  ],
  "abstract": "We extend the definition of conical representations for Riemannian symmetric spaces to a certain class of infinite-dimensional Riemannian symmetric spaces. Using an infinite-dimensional version of Weyl's Unitary Trick, there is a correspondence between smooth representations of infinite-dimensional noncompact-type Riemannian symmetric spaces and smooth representations of infinite-dimensional compact-type symmetric spaces. We classify all smooth conical representations which are unitary on the compact-type side. Finally, a new class of non-smooth unitary conical representations appears on the compact-type side which has no analogue in the finite-dimensional case. We classify these representations and show how to decompose them into direct integrals of irreducible conical representations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-22T18:21:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "43A85",
      "53C35",
      "22E46"
    ],
    "keywords": [
      "direct limits",
      "infinite-dimensional noncompact-type riemannian symmetric spaces",
      "non-smooth unitary conical representations appears",
      "compact-type side",
      "smooth representations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151107045D"
    }
  }
}