{
  "id": "1811.07581",
  "version": "v2",
  "published": "2018-11-19T09:50:55.000Z",
  "updated": "2019-04-13T03:28:24.000Z",
  "title": "Restricting Schubert classes to symplectic Grassmannians using self-dual puzzles",
  "authors": [
    "Iva Halacheva",
    "Allen Knutson",
    "Paul Zinn-Justin"
  ],
  "comment": "10 pages, FPSAC 2019 extended abstract. Incorporated referee reports and fixed some typos",
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "Given a Schubert class on $Gr(k,V)$ where $V$ is a symplectic vector space of dimension $2n$, we consider its restriction to the symplectic Grassmannian $SpGr(k,V)$ of isotropic subspaces. Pragacz gave tableau formulae for positively computing the expansion of these $H^*(Gr(k,V))$ classes into Schubert classes of the target when $k=n$, which corresponds to expanding Schur polynomials into $Q$-Schur polynomials. Coskun described an algorithm for their expansion when $k\\leq n$. We give a puzzle-based formula for these expansions, while extending them to equivariant cohomology. We make use of a new observation that usual Grassmannian puzzle pieces are already enough to do some $2$-step Schubert calculus, and apply techniques from quantum integrable systems (``scattering diagrams'').",
  "revisions": [
    {
      "version": "v2",
      "updated": "2019-04-13T03:28:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14M15",
      "05E10"
    ],
    "keywords": [
      "restricting schubert classes",
      "symplectic grassmannian",
      "self-dual puzzles",
      "usual grassmannian puzzle pieces",
      "pragacz gave tableau formulae"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}