{
  "id": "2012.04219",
  "version": "v1",
  "published": "2020-12-08T05:14:45.000Z",
  "updated": "2020-12-08T05:14:45.000Z",
  "title": "Formal degree and local theta correspondence; Quaternion case",
  "authors": [
    "Hirotala Kakuhama"
  ],
  "comment": "53 pages",
  "categories": [
    "math.NT",
    "math.RT"
  ],
  "abstract": "In this paper, we determine a constant from the local analogue of Siegel-Weil formula when at least one unitary groups are anisotropic, and describe the behavior of the formal degree under the local theta correspondence of nearly equal rank for quaternion dual pairs over a local field of characteristic $0$. As an application, we prove the formal degree conjecture of Hiraga-Ichino-Ikeda and Gross-Reeder for the non-split inner forms of ${\\rm Sp}_4$ and ${\\rm GSp}_4$. These results extend a work of Gan-Ichino to quaternion dual pairs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-08T05:14:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F27",
      "11F70"
    ],
    "keywords": [
      "local theta correspondence",
      "quaternion case",
      "quaternion dual pairs",
      "non-split inner forms",
      "formal degree conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 53,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}