{
  "id": "2310.10223",
  "version": "v1",
  "published": "2023-10-16T09:33:06.000Z",
  "updated": "2023-10-16T09:33:06.000Z",
  "title": "A Laurent phenomenon for the Cayley plane",
  "authors": [
    "Oliver Daisey",
    "Tom Ducat"
  ],
  "comment": "19 pages, 6 figures",
  "categories": [
    "math.AG"
  ],
  "abstract": "We describe a Laurent phenomenon for the Cayley plane, which is the homogeneous variety associated to the cominiscule representation of $E_6$. The corresponding Laurent phenomenon algebra has finite type and appears in a natural sequence of LPAs indexed by the $E_n$ Dynkin diagrams for $n \\leq 6$. We conjecture the existence of a further finite type LPA, associated to the Freudenthal variety of type $E_7$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-16T09:33:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cayley plane",
      "corresponding laurent phenomenon algebra",
      "finite type lpa",
      "dynkin diagrams",
      "natural sequence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}