{
  "id": "2306.14485",
  "version": "v1",
  "published": "2023-06-26T07:52:53.000Z",
  "updated": "2023-06-26T07:52:53.000Z",
  "title": "Combinatorics of semi-toric degenerations of Schubert varieties in type C",
  "authors": [
    "Naoki Fujita",
    "Yuta Nishiyama"
  ],
  "comment": "23 pages",
  "categories": [
    "math.CO",
    "math.AG",
    "math.RT"
  ],
  "abstract": "An approach to Schubert calculus is to realize Schubert classes as concrete combinatorial objects such as Schubert polynomials. Using the polytope ring of the Gelfand-Tsetlin polytopes, Kiritchenko-Smirnov-Timorin realized each Schubert class as a sum of reduced Kogan faces. The first named author introduced a generalization of reduced Kogan faces to symplectic Gelfand-Tsetlin polytopes using a semi-toric degeneration of a Schubert variety, and extended the result of Kiritchenko-Smirnov-Timorin to type C case. In this paper, we introduce a combinatorial model to this type C generalization using a kind of pipe dream with self-crossings. As an application, we prove that the type C generalization can be constructed by skew mitosis operators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-06-26T07:52:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E10",
      "14M15",
      "14N15"
    ],
    "keywords": [
      "schubert variety",
      "semi-toric degeneration",
      "reduced kogan faces",
      "combinatorics",
      "schubert class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}