{
  "id": "1710.04327",
  "version": "v1",
  "published": "2017-10-11T22:56:45.000Z",
  "updated": "2017-10-11T22:56:45.000Z",
  "title": "Jordan Decompositions of cocenters of reductive $p$-adic groups",
  "authors": [
    "Xuhua He",
    "Ju-lee Kim"
  ],
  "comment": "29 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "Cocenters of Hecke algebras $\\mathcal H$ play an important role in studying mod $\\ell$ or $\\mathbb C$ harmonic analysis on connected $p$-adic reductive groups. On the other hand, the depth $r$ Hecke algebra $\\mathcal H_{r^+}$ is well suited to study depth $r$ smooth representations. In this paper, we study depth $r$ rigid cocenters $\\overline{\\mathcal H}^{\\mathrm{rig}}_{r^+}$ of a connected reductive $p$-adic group over rings of characteristic zero or $\\ell\\neq p$. More precisely, under some mild hypotheses, we establish a Jordan decomposition of the depth $r$ rigid cocenter, hence find an explicit basis of $\\overline{\\mathcal H}^{\\mathrm{rig}}_{r^+}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-11T22:56:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E50",
      "11F70"
    ],
    "keywords": [
      "jordan decomposition",
      "adic group",
      "hecke algebra",
      "rigid cocenter",
      "study depth"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}