{
  "id": "math/0608546",
  "version": "v1",
  "published": "2006-08-22T15:53:32.000Z",
  "updated": "2006-08-22T15:53:32.000Z",
  "title": "A note on quantum products of Schubert classes in a Grassmannian",
  "authors": [
    "Dave Anderson"
  ],
  "comment": "9 pages, 4 figures",
  "categories": [
    "math.CO",
    "math.AG"
  ],
  "abstract": "Given two Schubert classes $\\sigma_{\\lambda}$ and $\\sigma_{\\mu}$ in the quantum cohomology of a Grassmannian, we construct a partition $\\nu$, depending on $\\lambda$ and $\\mu$, such that $\\sigma_{\\nu}$ appears with coefficient 1 in the lowest (or highest) degree part of the quantum product $\\sigma_{\\lambda}\\star\\sigma_{\\mu}$. To do this, we show that for any two partitions $\\lambda$ and $\\mu$, contained in a $k$-by-$(n-k)$ rectangle and such that the 180-degree rotation of one does not overlap the other, there is a third partition $\\nu$, also contained in the rectangle, such that the Littlewood-Richardson number $c_{\\lambda\\mu}^{\\nu}$ is 1.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-08-22T15:53:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E10",
      "14M15"
    ],
    "keywords": [
      "schubert classes",
      "quantum product",
      "grassmannian",
      "degree part",
      "quantum cohomology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......8546A"
    }
  }
}