{
  "id": "2210.13862",
  "version": "v1",
  "published": "2022-10-25T09:36:23.000Z",
  "updated": "2022-10-25T09:36:23.000Z",
  "title": "On a conjecture on 2-reduced Schur functions and Schur's Q-functions",
  "authors": [
    "Yuta Nishiyama"
  ],
  "comment": "27 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Motivated by Sato and Mori's work on the Korteweg-de Vries (KdV) equation and the modified KdV equation, Mizukawa, Nakajima, and Yamada made a conjecture on 2-reduced Schur functions and Schur's Q-functions. The conjecture claims that certain sums of products of a Littlewood-Richardson coefficient and two 2-reduced Schur functions are equal to Schur's Q-functions up to a scalar multiple. In this paper we give a proof of the conjecture in cases which have not been proved yet. We introduce a new expression of Schur's Q-functions and use it to prove the conjecture. Combinatorics of the inverse Kostka matrix is also used. We also provide consideration of the conjecture in general case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-25T09:36:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E05",
      "37K10",
      "05A10"
    ],
    "keywords": [
      "schurs q-functions",
      "schur functions",
      "inverse kostka matrix",
      "moris work",
      "korteweg-de vries"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}