{
  "id": "2301.09182",
  "version": "v1",
  "published": "2023-01-22T18:48:48.000Z",
  "updated": "2023-01-22T18:48:48.000Z",
  "title": "A comparison of endomorphism algebras",
  "authors": [
    "Kazuma Ohara"
  ],
  "comment": "94pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $F$ be a non-archimedean local field and $G$ be a connected reductive group over $F$. For a Bernstein block in the category of smooth complex representations of $G(F)$, we have two kinds of progenerators: the compactly induced representation $\\text{ind}_{K}^{G(F)} (\\rho)$ of a type $(K, \\rho)$, and the parabolically induced representation $I_{P}^{G}(\\Pi^{M})$ of a progenerator $\\Pi^{M}$ of a Bernstein block for a Levi subgroup $M$ of $G$. In this paper, we construct an explicit isomorphism of these two progenerators. Moreover, we compare the description of the endomorphism algebra $\\text{End}_{G(F)}\\left(\\text{ind}_{K}^{G(F)} (\\rho)\\right)$ for a depth-zero type $(K, \\rho)$ by Morris with the description of the endomorphism algebra $\\text{End}_{G(F)}\\left(I_{P}^{G}(\\Pi^{M})\\right)$ by Solleveld, that are described in terms of affine Hecke algebras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-22T18:48:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "endomorphism algebra",
      "bernstein block",
      "comparison",
      "affine hecke algebras",
      "smooth complex representations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 94,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}