{
  "id": "2101.03119",
  "version": "v1",
  "published": "2021-01-08T17:20:34.000Z",
  "updated": "2021-01-08T17:20:34.000Z",
  "title": "Real roots in the root system $\\mathsf{E}_{k,n}$",
  "authors": [
    "Karin Baur",
    "Jian-Rong Li",
    "Andrei Smolensky"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Motivated by the recent advances in the categorification of the cluster structure on the coordinate rings of Grassmannians of $k$-subspaces in $n$-space, we investigate a particular construction of root systems of type $\\mathsf{E}_{k,n}$, including the type $\\mathsf{E}_n$. This construction generalizes Manin's \"hyperbolic construction\" of $\\mathsf{E}_8$ and reveals a lot of otherwise hidden regularities in this family of root systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-08T17:20:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B22"
    ],
    "keywords": [
      "root system",
      "real roots",
      "construction generalizes manins",
      "coordinate rings",
      "cluster structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}