{
  "id": "1609.07456",
  "version": "v1",
  "published": "2016-09-23T18:31:18.000Z",
  "updated": "2016-09-23T18:31:18.000Z",
  "title": "Bounds on multiplicities of spherical spaces over finite fields",
  "authors": [
    "Avraham Aizenbud",
    "Nir Avni"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $G$ be a reductive group scheme of type $A$ acting on a spherical scheme $X$. We prove that there exists 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 $G(F)$. We give an explicit bound for $C$. We conjecture that this result is true for any reductive group scheme and when $F$ ranges (in addition) over all local fields of characteristic $0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-23T18:31:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C15",
      "20C15",
      "14M27"
    ],
    "keywords": [
      "finite field",
      "spherical spaces",
      "reductive group scheme",
      "multiplicity",
      "explicit bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}