{
  "id": "1511.05799",
  "version": "v1",
  "published": "2015-11-18T14:28:18.000Z",
  "updated": "2015-11-18T14:28:18.000Z",
  "title": "The absolute continuity of convolution products of orbital measures in exceptional symmetric spaces",
  "authors": [
    "Kathryn Hare",
    "Jimmy He"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $G$ be a non-compact group, $K$ the compact subgroup fixed by a Cartan involution and assume $G/K$ is an exceptional, symmetric space, one of Cartan type $E,F $ or $G$. We find the minimal integer, $L(G),$ such that any convolution product of $L(G)$ continuous, $K$-bi-invariant measures on $G$ is absolutely continuous with respect to Haar measure. Further, any product of $L(G)$ double cosets has non-empty interior. The number $L(G)$ is either $2$ or $3$% , depending on the Cartan type, and in most cases is strictly less than the rank of $G$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-18T14:28:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "43A80",
      "22E30",
      "53C35"
    ],
    "keywords": [
      "exceptional symmetric spaces",
      "convolution product",
      "orbital measures",
      "absolute continuity",
      "cartan type"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151105799H"
    }
  }
}