{
  "id": "2011.07408",
  "version": "v1",
  "published": "2020-11-14T22:55:23.000Z",
  "updated": "2020-11-14T22:55:23.000Z",
  "title": "Separating invariants over finite fields",
  "authors": [
    "Gregor Kemper",
    "Artem Lopatin",
    "Fabian Reimers"
  ],
  "comment": "18 pages",
  "categories": [
    "math.RT",
    "math.AC"
  ],
  "abstract": "We determine the minimal number of separating invariants for the invariant ring of a matrix group $G < \\mathrm{GL}_n(\\mathbb{F}_q)$ over the finite field $\\mathbb{F}_q$. We show that this minimal number can be obtained with invariants of degree at most $|G|n(q-1)$. In the non-modular case this construction can be improved to give invariants of degree at most $n(q-1)$. As examples we study separating invariants over the field $\\mathbb{F}_2$ for two important representations of the symmetric group",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-14T22:55:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13A50",
      "16R30",
      "20B30"
    ],
    "keywords": [
      "finite field",
      "minimal number",
      "study separating invariants",
      "matrix group",
      "symmetric group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}