{
  "id": "2204.05935",
  "version": "v1",
  "published": "2022-04-12T16:35:39.000Z",
  "updated": "2022-04-12T16:35:39.000Z",
  "title": "The twist for Richardson varieties",
  "authors": [
    "Pavel Galashin",
    "Thomas Lam"
  ],
  "comment": "37 pages, 4 figures",
  "categories": [
    "math.RT",
    "math.AG",
    "math.CO"
  ],
  "abstract": "We construct the twist automorphism of open Richardson varieties inside the flag variety of a complex semisimple algebraic group. We show that the twist map preserves totally positive parts, and prove a Chamber Ansatz formula for it. Our twist map generalizes the twist maps previously constructed by Berenstein-Fomin-Zelevinsky, Marsh-Scott, and Muller-Speyer. We use it to explain the relationship between the two conjectural cluster structures for Richardson varieties studied by Leclerc and by Ingermanson.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-12T16:35:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14M15",
      "13F60"
    ],
    "keywords": [
      "complex semisimple algebraic group",
      "open richardson varieties inside",
      "conjectural cluster structures",
      "map preserves totally positive parts",
      "twist map preserves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}