{
  "id": "2506.20038",
  "version": "v1",
  "published": "2025-06-24T22:29:52.000Z",
  "updated": "2025-06-24T22:29:52.000Z",
  "title": "Cluster structures in mixed Grassmanianns",
  "authors": [
    "Zenan Fu"
  ],
  "comment": "113 pages, 54 figures",
  "categories": [
    "math.CO",
    "math.AC",
    "math.RT"
  ],
  "abstract": "Generalizing the results by Fomin-Pylyavskyy and Carde, we construct a family of natural cluster structures in the coordinate ring of a mixed Grassmannian, the configuration space of tuples of several vectors and covectors in a finite-dimensional complex vector space. We describe and explore these cluster structures using the machinery of weaves introduced by Casals and Zaslow.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-06-24T22:29:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13F60",
      "05E99",
      "13A50",
      "14M15",
      "15A72",
      "15A75"
    ],
    "keywords": [
      "mixed grassmanianns",
      "finite-dimensional complex vector space",
      "natural cluster structures",
      "configuration space",
      "mixed grassmannian"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 113,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}