{
  "id": "1607.05640",
  "version": "v1",
  "published": "2016-07-19T15:48:58.000Z",
  "updated": "2016-07-19T15:48:58.000Z",
  "title": "Finite direct sums of cyclic embeddings and an application to invariant subspace varieties",
  "authors": [
    "Justyna Kosakowska",
    "Markus Schmidmeier"
  ],
  "categories": [
    "math.RT",
    "math.AG",
    "math.GR"
  ],
  "abstract": "In his 1951 book \"Infinite Abelian Groups\", Kaplansky gives a combinatorial characterization of the isomorphism types of embeddings of a cyclic subgroup in a finite abelian group. In this paper we use partial maps on Littlewood-Richardson tableaux to generalize this result to finite direct sums of such embeddings. As an application to invariant subspaces of nilpotent linear operators, we develop a critereon to decide if two irreducible components in the representation space are in the boundary partial order.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-19T15:48:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G10",
      "20K27",
      "14L30"
    ],
    "keywords": [
      "finite direct sums",
      "invariant subspace varieties",
      "cyclic embeddings",
      "application",
      "boundary partial order"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}