{
  "id": "2301.00529",
  "version": "v1",
  "published": "2023-01-02T05:09:39.000Z",
  "updated": "2023-01-02T05:09:39.000Z",
  "title": "Harmonic analysis on the fourfold cover of the space of ordered triangles I: the invariant differentials",
  "authors": [
    "Hanlong Fang",
    "Xiaocheng Li",
    "Yunfeng Zhang"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "Denote by $SL_n(\\mathbb R)$ the group of $n\\times n$ real matrices with determinant one, $A$ the subgroup consisting of the diagonal matrices with positive entries, and $SL_n(\\mathbb R)/A$ the manifold of left cosets $gA$, $g\\in SL_n(\\mathbb R)$. In this paper, we will be concerned with the harmonic analysis on the homogeneous space $SL_n(\\mathbb R)/A$ when $n=3$. In particular, we provide explicit generators and their relations for the algebra of the invariant differential operators. Then we prove that some of the non-central generators are essentially self-adjoint.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-02T05:09:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "43A85",
      "22E46",
      "22E30"
    ],
    "keywords": [
      "harmonic analysis",
      "fourfold cover",
      "ordered triangles",
      "invariant differential operators",
      "left cosets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}