{
  "id": "1605.09659",
  "version": "v1",
  "published": "2016-05-31T15:09:36.000Z",
  "updated": "2016-05-31T15:09:36.000Z",
  "title": "Fields of rationality of automorphic representations: the case of unitary groups",
  "authors": [
    "John Binder"
  ],
  "comment": "28 pages",
  "categories": [
    "math.NT",
    "math.RT"
  ],
  "abstract": "This paper examines fields of rationality in families of cuspidal automorphic representations of unitary groups. Specifically, for a fixed $A$ and a sufficiently large family $\\mathcal{F}$, a small proportion of representations $\\pi\\in \\mathcal{F}$ will satisfy $[\\mathbb{Q}(\\pi):\\mathbb{Q}] \\leq A$. Like earlier work of Shin and Templier, the result depends on a Plancherel equidistribution result for the local components of representations in families. An innovation of our work is an upper bound on the number of discrete series $GL_n(L)$ representations with small field of rationality, counted with appropriate multiplicity, which in turn depends upon an asymptotic character expansion of Murnaghan and formal degree computations of Aubert and Plymen.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-31T15:09:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "unitary groups",
      "rationality",
      "formal degree computations",
      "cuspidal automorphic representations",
      "asymptotic character expansion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}