{
  "id": "2109.01473",
  "version": "v1",
  "published": "2021-09-03T12:30:37.000Z",
  "updated": "2021-09-03T12:30:37.000Z",
  "title": "On the Left Connected Subalgebra of the Descent Algebra of a Coxeter Group of Classical Type",
  "authors": [
    "Linus Hellebrandt",
    "Götz Pfeiffer"
  ],
  "comment": "11 pages, comments welcome!",
  "categories": [
    "math.GR",
    "math.CO"
  ],
  "abstract": "A Coxeter group of classical type $A_n$, $B_n$ or $D_n$ contains a chain of subgroups of the same type. We show that intersections of conjugates of these subgroups are again of the same type, and make precise in which sense and to what extent this property is exclusive to the classical types of Coxeter groups. As the main tool for the proof we use Solomon's descent algebra. Using Stirling numbers, we express certain basis elements of the descent algebra as polynomials and derive explicit multiplication formulas for a commutative subalgebra of the descent algebra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-03T12:30:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F55",
      "05E16",
      "33C80"
    ],
    "keywords": [
      "coxeter group",
      "left connected subalgebra",
      "classical type",
      "derive explicit multiplication formulas",
      "solomons descent algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}