{
  "id": "1911.01880",
  "version": "v1",
  "published": "2019-11-05T15:38:55.000Z",
  "updated": "2019-11-05T15:38:55.000Z",
  "title": "Analytic newvectors for $\\mathrm{GL}_n(\\mathbb{R})$",
  "authors": [
    "Subhajit Jana",
    "Paul D. Nelson"
  ],
  "comment": "47 pages",
  "categories": [
    "math.NT",
    "math.RT"
  ],
  "abstract": "We relate the analytic conductor of a generic irreducible representation of $\\mathrm{GL}_n(\\mathbb{R})$ to the invariance properties of vectors in that representation. The relationship is an analytic archimedean analogue of some aspects of the classical non-archimedean newvector theory of Casselman and Jacquet--Piatetski-Shapiro--Shalika. We illustrate how this relationship may be applied in trace formulas to majorize sums over automorphic forms on $\\mathrm{PGL}_n(\\mathbb{Z}) \\backslash \\mathrm{PGL}_n(\\mathbb{R})$ ordered by analytic conductor.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-05T15:38:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F55",
      "22E50"
    ],
    "keywords": [
      "analytic newvectors",
      "analytic conductor",
      "analytic archimedean analogue",
      "classical non-archimedean newvector theory",
      "automorphic forms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 47,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}