{
  "id": "1809.08003",
  "version": "v1",
  "published": "2018-09-21T09:27:26.000Z",
  "updated": "2018-09-21T09:27:26.000Z",
  "title": "A classification of spherical Schubert varieties in the Grassmannian",
  "authors": [
    "Reuven Hodges",
    "Venkatramani Lakshmibai"
  ],
  "comment": "22 pages",
  "categories": [
    "math.RT",
    "math.AG",
    "math.CO"
  ],
  "abstract": "Let $L$ be a Levi subgroup of $GL_N$ which acts by left multiplication on a Schubert variety $X(w)$ in the Grassmannian $G_{d,N}$. We say that $X(w)$ is a spherical Schubert variety if $X(w)$ is a spherical variety for the action of $L$. In earlier work we provide a combinatorial description of the decomposition of the homogeneous coordinate ring of $X(w)$ into irreducible $L$-modules for the induced action of $L$. In this work we classify those decompositions into irreducible $L$-modules that are multiplicity-free. This is then applied towards giving a complete classification of the spherical Schubert varieties in the Grassmannian.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-21T09:27:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G05",
      "20G20",
      "14B05",
      "14M27"
    ],
    "keywords": [
      "spherical schubert variety",
      "grassmannian",
      "combinatorial description",
      "left multiplication",
      "earlier work"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}