{
  "id": "1412.5549",
  "version": "v1",
  "published": "2014-12-17T19:55:58.000Z",
  "updated": "2014-12-17T19:55:58.000Z",
  "title": "Cusp forms for exceptional group of type $E_{7}$",
  "authors": [
    "Henry H. Kim",
    "Takuya Yamauchi"
  ],
  "comment": "39 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\bf{G}$ be the connected reductive group of type $E_{7,3}$ over $\\mathbb{Q}$ and $\\mathfrak{T}$ be the corresponding symmetric domain in $\\mathbb{C}^{27}$. Let $\\Gamma=\\bf{G}(\\mathbb{Z})$ be the arithmetic subgroup defined by Baily. In this paper, for any positive integer $k\\ge 10$, we will construct a (non-zero) holomorphic cusp form on $\\mathfrak{T}$ of weight $2k$ with respect to $\\Gamma$ from a Hecke cusp form in $S_{2k-8}(SL_2(\\mathbb{Z}))$. This lift is an analogue of Ikeda's construction.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-17T19:55:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "exceptional group",
      "holomorphic cusp form",
      "hecke cusp form",
      "arithmetic subgroup",
      "corresponding symmetric domain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.5549K"
    }
  }
}