{
  "id": "1402.4435",
  "version": "v3",
  "published": "2014-02-18T18:44:27.000Z",
  "updated": "2015-01-05T10:28:38.000Z",
  "title": "Cluster structures on strata of flag varieties",
  "authors": [
    "Bernard Leclerc"
  ],
  "comment": "31 pages, v.2 : a comment about the relation to Muller-Speyer conjecture on positroid varieties is added in 7.3. v.3. final version, to appear in Advances in Math",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "We introduce some new Frobenius subcategories of the module category of a preprojective algebra of Dynkin type, and we show that they have a cluster structure in the sense of Buan-Iyama-Reiten-Scott. These categorical cluster structures yield cluster algebra structures in the coordinate rings of intersections of opposed Schubert cells.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-03-21T17:30:05.000Z",
      "comment": "31 pages, v.2 : a comment about the relation to Muller-Speyer conjecture on positroid varieties is added in 7.3",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-01-05T10:28:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "flag varieties",
      "cluster structures yield cluster algebra",
      "structures yield cluster algebra structures",
      "categorical cluster structures yield cluster",
      "dynkin type"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.4435L"
    }
  }
}