{
  "id": "1712.07985",
  "version": "v1",
  "published": "2017-12-21T14:54:48.000Z",
  "updated": "2017-12-21T14:54:48.000Z",
  "title": "A McKay correspondence for the Poincaré series of some finite subgroups of ${\\rm SL}_3(\\CC)$",
  "authors": [
    "Wolfgang Ebeling"
  ],
  "comment": "11 pages",
  "categories": [
    "math.AG",
    "math.RT"
  ],
  "abstract": "A finite subgroup of ${\\rm SL}_2(\\CC)$ defines a (Kleinian) rational surface singularity. The McKay correspondence yields a relation between the Poincar\\'e series of the algebra of invariants of such a group and the characteristic polynomials of certain Coxeter elements determined by the corresponding singularity. Here we consider some non-abelian finite subgroups $G$ of ${\\rm SL}_3(\\CC)$. They define non-isolated three-dimensional Gorenstein quotient singularities. We consider suitable hyperplane sections of such singularities which are Kleinian or Fuchsian surface singularities. We show that we obtain a similar relation between the group $G$ and the corresponding surface singularity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-21T14:54:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32S25",
      "14E16",
      "13A50",
      "20G05"
    ],
    "keywords": [
      "surface singularity",
      "define non-isolated three-dimensional gorenstein quotient",
      "non-isolated three-dimensional gorenstein quotient singularities",
      "non-abelian finite subgroups",
      "fuchsian surface singularities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}