{
  "id": "1510.01528",
  "version": "v1",
  "published": "2015-10-06T11:08:34.000Z",
  "updated": "2015-10-06T11:08:34.000Z",
  "title": "Higher ramification and the local Langlands correspondence",
  "authors": [
    "Colin J. Bushnell",
    "Guy Henniart"
  ],
  "categories": [
    "math.NT",
    "math.RT"
  ],
  "abstract": "Let $F$ be a non-Archimedean locally compact field. We show that the local Langlands correspondence over $F$ has a strong property generalizing the higher ramification theorem of local class field theory. If $\\pi$ is an irreducible cuspidal representation of a general linear group $GL_n(F)$ and $\\sigma$ the corresponding irreducible representation of the Weil group $W_F$ of $F$, the restriction of $\\sigma$ to a ramification subgroup of $W_F$ is determined by a truncation of the simple character $\\theta_\\pi$ contained in $\\pi$, and conversely. Numerical aspects of the relation are governed by a Herbrand-like function $\\Psi_\\Theta$ depending on the endo-class $\\Theta$ of $\\theta_\\pi$. We give a method for determining $\\Psi_\\Theta$. Consequently, the ramification-theoretic structure of $\\sigma$ can be predicted from the simple character $\\theta_\\pi$ alone.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-06T11:08:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E50",
      "11S37",
      "11S15"
    ],
    "keywords": [
      "local langlands correspondence",
      "local class field theory",
      "simple character",
      "higher ramification theorem",
      "non-archimedean locally compact field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}