{
  "id": "1504.04657",
  "version": "v1",
  "published": "2015-04-17T23:04:35.000Z",
  "updated": "2015-04-17T23:04:35.000Z",
  "title": "Kraśkiewicz-Pragacz modules and Ringel duality",
  "authors": [
    "Masaki Watanabe"
  ],
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "Kra\\'skiewicz and Pragacz introduced representations of the upper-triangular Lie algebras whose characters are Schubert polynomials. In previous works the author studied the structure of Kra\\'skiewicz-Pragacz modules using the theory of highest weight categories. From the results there, in particular we obtain a certain highest weight category whose standard modules are KP modules. In this paper we show that this highest weight category is self Ringel-dual, and shows that the tensor product operation on $\\mathfrak{b}$-modules is compatible with Ringel duality functor.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-17T23:04:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "highest weight category",
      "kraśkiewicz-pragacz modules",
      "upper-triangular lie algebras",
      "tensor product operation",
      "ringel duality functor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150404657W"
    }
  }
}