{
  "id": "2306.10390",
  "version": "v1",
  "published": "2023-06-17T16:52:48.000Z",
  "updated": "2023-06-17T16:52:48.000Z",
  "title": "Determinantal expressions of certain integrals on symmetric spaces",
  "authors": [
    "Salem Said",
    "Cyrus Mostajeran"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "The integral of a function $f$ defined on a symmetric space $M \\simeq G/K$ may be expressed in the form of a determinant (or Pfaffian), when $f$ is $K$-invariant and, in a certain sense, a tensor power of a positive function of a single variable. The paper presents a few examples of this idea and discusses future extensions. Specifically, the examples involve symmetric cones, Grassmann manifolds, and classical domains.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-06-17T16:52:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "symmetric space",
      "determinantal expressions",
      "tensor power",
      "symmetric cones",
      "grassmann manifolds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}