{
  "id": "1907.09975",
  "version": "v1",
  "published": "2019-07-23T16:01:41.000Z",
  "updated": "2019-07-23T16:01:41.000Z",
  "title": "Hopf algebra structure of symmetric and quasisymmetric functions in superspace",
  "authors": [
    "Susanna Fishel",
    "Luc Lapointe",
    "Maria Elena Pinto"
  ],
  "journal": "J. Combin. Theory Ser. A 166 (2019), 144-170",
  "categories": [
    "math.CO"
  ],
  "abstract": "We show that the ring of symmetric functions in superspace is a cocommutative and self-dual Hopf algebra. We provide formulas for the action of the coproduct and the antipode on various bases of that ring. We introduce the ring sQSym of quasisymmetric functions in superspace and show that it is a Hopf algebra. We give explicitly the product, coproduct and antipode on the basis of monomial quasisymmetric functions in superspace. We prove that the Hopf dual of sQSym, the ring sNSym of noncommutative symmetric functions in superspace, has a multiplicative basis dual to the monomial quasisymmetric functions in superspace.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-23T16:01:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hopf algebra structure",
      "superspace",
      "monomial quasisymmetric functions",
      "self-dual hopf algebra",
      "noncommutative symmetric functions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}