{
  "id": "1711.08860",
  "version": "v1",
  "published": "2017-11-24T02:33:00.000Z",
  "updated": "2017-11-24T02:33:00.000Z",
  "title": "Positivity of principal matrix coefficients of principal series representations of $GL_{n}(R)$",
  "authors": [
    "Yangyang Chen"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $G=GL_{n}(R)$, with the usual Cartan decomposition $G=Kexp(p_0)$ and the usual Iwasawa decomposition $G=NAK$. We determine the image of $exp(p_0)$ under the projection of $G$ to $K$ through the Iwasawa decomposition. As an application, we prove a positivity result about the matrix coefficients of principal series representations of $G$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-24T02:33:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "principal series representations",
      "principal matrix coefficients",
      "usual iwasawa decomposition",
      "usual cartan decomposition",
      "positivity result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}