{
  "id": "0712.2614",
  "version": "v4",
  "published": "2007-12-17T01:53:21.000Z",
  "updated": "2010-11-23T15:24:59.000Z",
  "title": "Characters of unipotent groups over finite fields",
  "authors": [
    "Mitya Boyarchenko"
  ],
  "comment": "Version 4, 81 pages, LaTeX. Main change compared to the previous version: the term \"$L$-packet\" has been replaced with \"$\\mathbb{L}$-packet\", which is short for \"Lusztig packet\" (to distinguish it from Langlands' notion of an $L$-packet)",
  "journal": "Selecta Mathematica, Vol. 16 (2010), No. 4, pp. 857--933",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let G be a connected unipotent group over a finite field F_q with q elements. In this article we propose a definition of L-packets of complex irreducible representations of the finite group G(F_q) and give an explicit description of L-packets in terms of the so-called \"admissible pairs\" for G. We then apply our results to show that if the centralizer of every geometric point of G is connected, then the dimension of every complex irreducible representation of G(F_q) is a power of q, confirming a conjecture of V. Drinfeld. This paper is the first in a series of three papers exploring the relationship between representations of a group of the form G(F_q) (where G is a unipotent algebraic group over F_q), the geometry of G, and the theory of character sheaves.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2010-11-23T15:24:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite field",
      "complex irreducible representation",
      "unipotent algebraic group",
      "connected unipotent group",
      "geometric point"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 81,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0712.2614B"
    }
  }
}