{
  "id": "1003.2742",
  "version": "v1",
  "published": "2010-03-13T21:17:08.000Z",
  "updated": "2010-03-13T21:17:08.000Z",
  "title": "Representations of unipotent groups over local fields and Gutkin's conjecture",
  "authors": [
    "Mitya Boyarchenko"
  ],
  "comment": "20 pages, LaTeX",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let F be a finite field or a local field of any characteristic. If A is a finite dimensional associative nilpotent algebra over F, the set 1+A of all formal expressions of the form 1+x, where x ranges over the elements of A, is a locally compact group with the topology induced by the standard one on F and the multiplication given by (1+x)(1+y)=1+(x+y+xy). We prove a result conjectured by Eugene Gutkin in 1973: every unitary irreducible representation of 1+A can be obtained by unitary induction from a 1-dimensional unitary character of a subgroup of the form 1+B, where B is an F-subalgebra of A. In the case where F is local and nonarchimedean we also establish an analogous result for smooth irreducible representations of 1+A over the field of complex numbers and show that every such representation is admissible and carries an invariant Hermitian inner product.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-03-13T21:17:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "local field",
      "gutkins conjecture",
      "unipotent groups",
      "invariant hermitian inner product",
      "finite dimensional associative nilpotent algebra"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1003.2742B"
    }
  }
}