{
  "id": "2210.15190",
  "version": "v1",
  "published": "2022-10-27T05:49:41.000Z",
  "updated": "2022-10-27T05:49:41.000Z",
  "title": "The center of Hecke algebras of types",
  "authors": [
    "Reda Boumasmoud",
    "Radhika Ganapathy"
  ],
  "comment": "23 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "We describe the center of the Hecke algebra of a type attached to a Bernstein block under some hypothesis. When $\\bf G$ is a connected reductive group over non-archimedean local field $F$ that splits over a tamely ramified extension of $F$ and the residue characteristic of $F$ does not divide the order of the absolute Weyl group of $\\bf G$, the works of Kim-Yu and Fintzen associate a type to each Bernstein block and our hypothesis is satisfied for such types. We use our results to give a description of the Bernstein center of the Hecke algebra $\\mathcal{H}({\\bf G } (F),K)$ when $K$ belongs to a nice family of compact open subgroups of ${\\bf G}(F)$ (which includes all the Moy-Prasad filtrations of an Iwahori subgroup) via the theory of types.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-27T05:49:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hecke algebra",
      "bernstein block",
      "non-archimedean local field",
      "absolute weyl group",
      "compact open subgroups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}