{
  "id": "1602.04602",
  "version": "v1",
  "published": "2016-02-15T09:55:24.000Z",
  "updated": "2016-02-15T09:55:24.000Z",
  "title": "Generic irreducibilty of Laplace eigenspaces on certain compact Lie groups",
  "authors": [
    "Dorothee Schueth"
  ],
  "comment": "13 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "If $G$ is a compact Lie group endowed with a left invariant metric $g$, then $G$ acts via pullback by isometries on each eigenspace of the associated Laplace operator $\\Delta_g$. We establish algebraic criteria for the existence of left invariant metrics $g$ on $G$ such that each eigenspace of $\\Delta_g$, regarded as the real vector space of the corresponding real eigenfunctions, is irreducible under the action of $G$. We prove that generic left invariant metrics on the Lie groups $G=\\operatorname{SU}(2)\\times\\ldots\\times\\operatorname{SU}(2)\\times T$, where $T$ is a (possibly trivial) torus, have the property just described. The same holds for quotients of such groups $G$ by discrete central subgroups. In particular, it also holds for $\\operatorname{SO}(3)$, $\\operatorname{U}(2)$, $\\operatorname{SO}(4)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-15T09:55:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58J50",
      "53C30",
      "22E46"
    ],
    "keywords": [
      "compact lie group",
      "laplace eigenspaces",
      "generic irreducibilty",
      "generic left invariant metrics",
      "discrete central subgroups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160204602S"
    }
  }
}