{
  "id": "2205.05252",
  "version": "v1",
  "published": "2022-05-11T03:44:59.000Z",
  "updated": "2022-05-11T03:44:59.000Z",
  "title": "Unicity of types and local Jacquet--Langlands correspondence",
  "authors": [
    "Yuki Yamamoto"
  ],
  "comment": "5 pages",
  "categories": [
    "math.RT",
    "math.NT"
  ],
  "abstract": "Let $F$ be a non-archimedean local field. For any irreducible representation $\\pi$ of an inner form $G'=\\mathrm{GL}_{m}(D)$ of $G=\\mathrm{GL}_{N}(F)$, there exists an irredubile representation of a maximal compact open subgroup in $G'$ which is also a type for $\\pi$. Then we can consider the problem whether these types are unique or not in some sense. If such types for $\\pi$ are unique, we say $\\pi$ has the strong unicity property of types. On the other hand, there exists a correspondence connecting irreducible representations of $G'$ and $G$, called the Jacquet--Langland correspondence. In this paper, we study the ralation between the strong unicity of types and the Jacquet--Langlands correspondence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-11T03:44:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E50"
    ],
    "keywords": [
      "local jacquet-langlands correspondence",
      "maximal compact open subgroup",
      "non-archimedean local field",
      "strong unicity property",
      "jacquet-langland correspondence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}