{
  "id": "1912.03694",
  "version": "v1",
  "published": "2019-12-08T15:20:21.000Z",
  "updated": "2019-12-08T15:20:21.000Z",
  "title": "Bounds on multiplicities of spherical spaces over finite fields -- the general case",
  "authors": [
    "Shai Shechter"
  ],
  "comment": "11 pages, comments welcome",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $G$ be a connected reductive group scheme acting on a spherical scheme $X$. In the case where $G$ is of type $A_n$, Aizenbud and Avni proved the existence of a number $C$ such that the multiplicity $\\dim\\hom(\\rho,\\mathbb{C}[X(F)])$ is bounded by $C$, for any finite field $F$ and any irreducible representation $\\rho$ of $G(F)$. In this paper, we generalize this result to the case where $G$ is a connected reductive group scheme over $\\mathbb{Z}$, and prove Conjecture A of [1].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-08T15:20:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite field",
      "general case",
      "spherical spaces",
      "connected reductive group scheme",
      "multiplicity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}