{
  "id": "2104.04876",
  "version": "v1",
  "published": "2021-04-10T23:16:44.000Z",
  "updated": "2021-04-10T23:16:44.000Z",
  "title": "The Langlands-Shahidi method for pairs via types and covers",
  "authors": [
    "Yeongseong Jo",
    "Muthu Krishnamurthy"
  ],
  "categories": [
    "math.RT",
    "math.NT"
  ],
  "abstract": "We compute the local coefficient attached to a pair $(\\pi_1,\\pi_2)$ of supercuspidal (complex) representations of the general linear group using the theory of types and covers \\`{a} la Bushnell-Kutzko. In the process, we obtain another proof of a well-known formula of Shahidi for the corresponding Plancherel constant. The approach taken here can be adapted to other situations of arithmetic interest within the context of the Langlands-Shahidi method, particularly, to that of a Siegel Levi subgroup inside a classical group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-10T23:16:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "langlands-shahidi method",
      "siegel levi subgroup inside",
      "general linear group",
      "approach taken",
      "local coefficient"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}