{
  "id": "1205.6448",
  "version": "v2",
  "published": "2012-05-29T18:57:48.000Z",
  "updated": "2015-11-02T04:50:05.000Z",
  "title": "Lifting representations of finite reductive groups: a character relation",
  "authors": [
    "Jeffrey D. Adler",
    "Michael Cassel",
    "Joshua M. Lansky",
    "Emma Morgan",
    "Yifei Zhao"
  ],
  "comment": "Minor errors corrected, proofs streamlined. Main result slightly generalized, restated to emphasize analogy with stability",
  "categories": [
    "math.RT"
  ],
  "abstract": "Given a connected reductive group $\\tilde{G}$ over a finite field $k$, and a semisimple $k$-automorphism $\\varepsilon$ of $\\tilde{G}$ of finite order, let $G$ denote the connected part of the group of $\\varepsilon$-fixed points. Then there exists a lifting from packets of representations of $G(k)$ to packets for $\\tilde{G}(k)$. In the case of Deligne-Lusztig representations, we show that this lifting satisfies a character relation analogous to that of Shintani.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-05-29T18:57:48.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-11-02T04:50:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C33",
      "20G40"
    ],
    "keywords": [
      "finite reductive groups",
      "character relation",
      "lifting representations",
      "finite field",
      "finite order"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.6448A"
    }
  }
}