{
  "id": "2010.08408",
  "version": "v1",
  "published": "2020-10-16T14:08:45.000Z",
  "updated": "2020-10-16T14:08:45.000Z",
  "title": "Galois representations for even general special orthogonal groups",
  "authors": [
    "Arno Kret",
    "Sug Woo Shin"
  ],
  "categories": [
    "math.NT",
    "math.RT"
  ],
  "abstract": "We prove the existence of $\\mathrm{GSpin}_{2n}$-valued Galois representations corresponding to cohomological cuspidal automorphic representations of certain quasi-split forms of $\\mathrm{GSO}_{2n}$ under the local hypotheses that there is a Steinberg component and that the archimedean parameters are regular for the standard representation. This is based on the cohomology of Shimura varieties of abelian type, of type $D^{\\mathbb{H}}$, arising from forms of $\\mathrm{GSO}_{2n}$. As an application, under similar hypotheses, we compute automorphic multiplicities, prove meromorphic continuation of (half) spin $L$-functions, and improve on the construction of $\\mathrm{SO}_{2n}$-valued Galois representations by removing the outer automorphism ambiguity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-16T14:08:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "general special orthogonal groups",
      "valued galois representations",
      "cohomological cuspidal automorphic representations",
      "outer automorphism ambiguity",
      "quasi-split forms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}