{
  "id": "2402.03552",
  "version": "v1",
  "published": "2024-02-05T22:12:14.000Z",
  "updated": "2024-02-05T22:12:14.000Z",
  "title": "Lowest $K$-types in the local Langlands correspondence",
  "authors": [
    "Jeffrey Adams",
    "Alexandre Afgoustidis"
  ],
  "comment": "42 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "Consider the irreducible representations of a real reductive group $G(\\mathbb{R})$, and their parametrization by the local Langlands correspondence. We ask: does the parametrization give easily accessible information on the restriction of representations to a maximal compact subgroup $K(\\mathbb{R})$ of $G(\\mathbb{R})$? We find a natural connection between the set of lowest $K$-types of a representation and its Langlands parameters. For our results, it is crucial to use the refined version of the local Langlands correspondence, involving (coverings of) component groups attached to $L$-homomorphisms. The first part of the paper is a simplified description of this refined parametrization.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-02-05T22:12:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E47",
      "22E50",
      "20G05"
    ],
    "keywords": [
      "local langlands correspondence",
      "maximal compact subgroup",
      "natural connection",
      "real reductive group",
      "langlands parameters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}