{
  "id": "1910.14639",
  "version": "v1",
  "published": "2019-10-31T17:29:04.000Z",
  "updated": "2019-10-31T17:29:04.000Z",
  "title": "Smooth representations of unit groups of split basic algebras over non-Archimedean local fields",
  "authors": [
    "Carlos A. M. André",
    "João Dias"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "We consider smooth representations of the unit group $G = \\mathcal{A}^{\\times}$ of a finite-dimensional split basic algebra $\\mathcal{A}$ over a non-Archimedean local field. In particular, we prove a version of Gutkin's conjecture, namely, we prove that every irreducible smooth representation of $G$ is compactly induced by a one-dimensional representation of the unit group of some subalgebra of $\\mathcal{A}$. We also discuss admissibility and unitarisability of smooth representations of G.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-31T17:29:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G25",
      "22D12",
      "22D30"
    ],
    "keywords": [
      "non-archimedean local field",
      "unit group",
      "finite-dimensional split basic algebra",
      "one-dimensional representation",
      "gutkins conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}