{
  "id": "1701.02417",
  "version": "v1",
  "published": "2017-01-10T02:30:50.000Z",
  "updated": "2017-01-10T02:30:50.000Z",
  "title": "Explicit asymptotic expansions for tame supercuspidal characters",
  "authors": [
    "Loren Spice"
  ],
  "comment": "74 pp",
  "categories": [
    "math.RT"
  ],
  "abstract": "We combine the ideas of a Harish-Chandra--Howe local character expansion, which can be centred at an arbitrary semisimple element, and a Kim--Murnaghan asymptotic expansion, which so far has been considered only around the identity. We show that, for most smooth, irreducible representations (those containing a good, minimal K-type), Kim--Murnaghan-type asymptotic expansions are valid on explicitly defined neighbourhoods of nearly arbitrary semisimple elements. We then give an explicit, inductive recipe for computing the coefficients in an asymptotic expansion for a tame supercuspidal representation. The only additional information needed in the inductive step is a fourth root of unity, which we expect to be useful in proving stability and endoscopic-transfer identities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-10T02:30:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E50",
      "22E35"
    ],
    "keywords": [
      "explicit asymptotic expansions",
      "tame supercuspidal characters",
      "arbitrary semisimple element",
      "harish-chandra-howe local character expansion",
      "kim-murnaghan asymptotic expansion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 74,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}