{
  "id": "2008.05296",
  "version": "v1",
  "published": "2020-08-12T13:20:40.000Z",
  "updated": "2020-08-12T13:20:40.000Z",
  "title": "Invariant measures for horospherical actions and Anosov groups",
  "authors": [
    "Minju Lee",
    "Hee Oh"
  ],
  "comment": "47 pages, 1 figure",
  "categories": [
    "math.DS",
    "math.GT"
  ],
  "abstract": "Let $\\Gamma$ be an Anosov subgroup of a connected semisimple real linear Lie group $G$. For a maximal horospherical subgroup $N$ of $G$, we show that the space of all non-trivial $NM$-invariant ergodic and $A$-quasi-invariant Radon measures on $\\Gamma\\backslash G$, up to proportionality, is homeomorphic to ${\\mathbb R}^{\\text{rank}\\,G-1}$, where $A$ is a maximal real split torus and $M$ is a maximal compact subgroup which normalizes $N$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-12T13:20:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "anosov groups",
      "invariant measures",
      "horospherical actions",
      "semisimple real linear lie group",
      "connected semisimple real linear lie"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 47,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}