{
  "id": "2408.07012",
  "version": "v1",
  "published": "2024-08-13T16:20:32.000Z",
  "updated": "2024-08-13T16:20:32.000Z",
  "title": "An LLL algorithm with symmetries",
  "authors": [
    "Beth Romano",
    "Jack A. Thorne"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We give a generalisation of the Lenstra-Lenstra-Lov\\'asz (LLL) lattice-reduction algorithm that is valid for an arbitrary (split, semisimple) reductive group $G$. This can be regarded as `lattice reduction with symmetries'. We make this algorithm explicit for the classical groups $G = \\mathrm{Sp}_{2g}$, $\\mathrm{SO}_{2g}$, and for the exceptional group $G = G_2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-13T16:20:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lll algorithm",
      "symmetries",
      "lattice reduction",
      "exceptional group",
      "lattice-reduction algorithm"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}