{
  "id": "1001.5296",
  "version": "v1",
  "published": "2010-01-28T23:44:45.000Z",
  "updated": "2010-01-28T23:44:45.000Z",
  "title": "On the computability of some positive-depth supercuspidal characters near the identity",
  "authors": [
    "Raf Cluckers",
    "Clifton Cunningham",
    "Julia Gordon",
    "Loren Spice"
  ],
  "categories": [
    "math.RT",
    "math.LO"
  ],
  "abstract": "This paper is concerned with the values of Harish-Chandra characters of a class of positive-depth, toral, very supercuspidal representations of $p$-adic symplectic and special orthogonal groups, near the identity element. We declare two representations equivalent if their characters coincide on a specific neighbourhood of the identity (which is larger than the neighbourhood on which Harish-Chandra local character expansion holds). We construct a parameter space $B$ (that depends on the group and a real number $r>0$) for the set of equivalence classes of the representations of minimal depth $r$ satisfying some additional assumptions. This parameter space is essentially a geometric object defined over $\\Q$. Given a non-Archimedean local field $\\K$ with sufficiently large residual characteristic, the part of the character table near the identity element for $G(\\K)$ that comes from our class of representations is parameterized by the residue-field points of $B$. The character values themselves can be recovered by specialization from a constructible motivic exponential function. The values of such functions are algorithmically computable. It is in this sense that we show that a large part of the character table of the group $G(\\K)$ is computable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-01-28T23:44:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E50",
      "03C98"
    ],
    "keywords": [
      "positive-depth supercuspidal characters",
      "harish-chandra local character expansion holds",
      "identity element",
      "representations",
      "parameter space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1001.5296C"
    }
  }
}