{
  "id": "1606.08872",
  "version": "v1",
  "published": "2016-06-28T20:21:19.000Z",
  "updated": "2016-06-28T20:21:19.000Z",
  "title": "Fourier Coefficients for Degenerate Eisenstein Series and the Descending Decomposition",
  "authors": [
    "Yuanqing Cai"
  ],
  "categories": [
    "math.RT",
    "math.CO",
    "math.NT"
  ],
  "abstract": "We determine the unipotent orbits attached to degenerate Eisenstein series on general linear groups. This confirms a conjecture of David Ginzburg. This also shows that any unipotent orbit of general linear groups does occur as the unipotent orbit attached to a specific automorphic representation. The key ingredient is a root-theoretic result. To prove it, we introduce the notion of the descending decomposition, which expresses every Weyl group element as a product of simple reflections in a certain way. It is suitable for induction and allows us to translate the question into a combinatorial statement.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-28T20:21:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F30",
      "11F70",
      "05E10",
      "22E50",
      "22E55"
    ],
    "keywords": [
      "degenerate eisenstein series",
      "descending decomposition",
      "fourier coefficients",
      "unipotent orbit",
      "general linear groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}