{
  "id": "1909.10748",
  "version": "v1",
  "published": "2019-09-24T07:53:48.000Z",
  "updated": "2019-09-24T07:53:48.000Z",
  "title": "On the types for supercuspidal representations of inner forms of $\\mathrm{GL}_{N}$",
  "authors": [
    "Yuki Yamamoto"
  ],
  "comment": "28 pages",
  "categories": [
    "math.NT",
    "math.RT"
  ],
  "abstract": "Let $F$ be a non-Archimedean local field, $A$ be a central simple $F$-algebra, and $G$ be the multiplicative group of $A$. It is known that for every irreducible supercuspidal representation $\\pi$, there exists a $[G, \\pi]_{G}$-type $(J, \\lambda)$, called a (maximal) simple type. We will show that $[G, \\pi]_{G}$-types defined over some maximal compact subgroup are unique up to $G$-conjugations under some unramifiedness assumption on a simple stratum.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-24T07:53:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "inner forms",
      "non-archimedean local field",
      "maximal compact subgroup",
      "simple stratum",
      "central simple"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}