{
  "id": "1806.04984",
  "version": "v1",
  "published": "2018-06-13T12:38:45.000Z",
  "updated": "2018-06-13T12:38:45.000Z",
  "title": "Slopes of Euclidean lattices, tensor product and group actions",
  "authors": [
    "Renaud Coulangeon",
    "Gabriele Nebe"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We study the behaviour of the minimal slope of Euclidean lattices under tensor product. A general conjecture predicts that $\\mu_{min}(L \\otimes M) = \\mu_{min}(L)\\mu_{min}(M)$ for all Euclidean lattices $L$ and $M$. We prove that this is the case under the additional assumptions that $L$ and $M$ are acted on multiplicity-free by their automorphism group, such that one of them has at most $2$ irreducible components.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-13T12:38:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11E39",
      "11H55"
    ],
    "keywords": [
      "euclidean lattices",
      "tensor product",
      "group actions",
      "general conjecture predicts",
      "automorphism group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}