{
  "id": "2212.02037",
  "version": "v1",
  "published": "2022-12-05T05:13:51.000Z",
  "updated": "2022-12-05T05:13:51.000Z",
  "title": "A generalization of the Murnaghan-Nakayama rule for $K$-$k$-Schur and $k$-Schur functions",
  "authors": [
    "Duc-Khanh Nguyen"
  ],
  "comment": "19 pages, 4 pictures",
  "categories": [
    "math.RT",
    "math.CO",
    "math.KT"
  ],
  "abstract": "We introduce a generalization of $K$-$k$-Schur functions and $k$-Schur functions via the Pieri rule. Then we obtain the Murnaghan-Nakayama rule for the generalized functions. The rule are described explicitly in the cases of $K$-$k$-Schur functions and $k$-Schur functions, with concrete descriptions and algorithms for coefficients. Our work recovers the result of Bandlow, Schilling, and Zabrocki for $k$-Schur functions, and explains it as a degeneration of the rule for $K$-$k$-Schur functions. In particular, many other special cases promise to be detailed in the future.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-05T05:13:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E05",
      "14N15"
    ],
    "keywords": [
      "schur functions",
      "murnaghan-nakayama rule",
      "generalization",
      "special cases promise",
      "concrete descriptions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}