{
  "id": "2411.09862",
  "version": "v1",
  "published": "2024-11-15T00:48:45.000Z",
  "updated": "2024-11-15T00:48:45.000Z",
  "title": "Schubert cells and Whittaker functionals for $\\text{GL}(n,\\mathbb{R})$ part II: Existence via integration by parts",
  "authors": [
    "Doyon Kim"
  ],
  "comment": "35 pages. arXiv admin note: text overlap with arXiv:2410.13519",
  "categories": [
    "math.RT",
    "math.NT"
  ],
  "abstract": "We give a new proof of the existence of Whittaker functionals for principal series representation of $\\text{GL}(n,\\mathbb{R})$, utilizing the analytic theory of distributions. We realize Whittaker functionals as equivariant distributions on $\\text{GL}(n,\\mathbb{R})$, whose restriction to the open Schubert cell is unique up to a constant. Using a birational map on the Schubert cells, we show that the unique distribution on the open Schubert cell extends to a distribution on the entire space $\\text{GL}(n,\\mathbb{R})$. This technique gives a proof of the analytic continuation of Jacquet integrals via integration by parts.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-11-15T00:48:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F70",
      "46F10"
    ],
    "keywords": [
      "whittaker functionals",
      "integration",
      "open schubert cell extends",
      "principal series representation",
      "equivariant distributions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}