{
  "id": "2008.08864",
  "version": "v1",
  "published": "2020-08-20T09:50:28.000Z",
  "updated": "2020-08-20T09:50:28.000Z",
  "title": "Bigrassmannian permutations and Verma modules",
  "authors": [
    "Hankyung Ko",
    "Volodymyr Mazorchuk",
    "Rafael Mrđen"
  ],
  "comment": "18 pages",
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "We show that bigrassmannian permutations determine the socle of the cokernel of an inclusion of Verma modules in type $A$. All such socular constituents turn out to be indexed by Weyl group elements from the penultimate two-sided cell. Combinatorially, the socular constituents in the cokernel of the inclusion of a Verma module indexed by $w\\in S_n$ into the dominant Verma module are shown to be determined by the essential set of $w$ and their degrees in the graded picture are shown to be computable in terms of the associated rank function. As an application, we compute the first extension from a simple module to a Verma module.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-20T09:50:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dominant verma module",
      "weyl group elements",
      "bigrassmannian permutations determine",
      "socular constituents turn",
      "simple module"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}