{
  "id": "1705.06478",
  "version": "v1",
  "published": "2017-05-18T08:57:45.000Z",
  "updated": "2017-05-18T08:57:45.000Z",
  "title": "Dirac cohomology, the projective supermodules of the symmetric group and the Vogan morphism",
  "authors": [
    "Kieran Calvert"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "In this paper we will derive an explicit description of the genuine projective representations of the symmetric group $S_n$ using Dirac cohomology and the branching graph for the irreducible genuine projective representations of $S_n$. In 2015 Ciubotaru and He, using the extended Dirac index, showed that the characters of the projective representations of $S_n$ are related to the characters of elliptic graded modules. We derived the branching graph using Dirac theory and combinatorics relating to the cohomology of Borel varieties $\\mathcal{B}_e$ of $\\mathfrak{g}$ and were able to use Dirac cohomology to construct an explicit model for the projective representations. We also described Vogan's morphism for Hecke algebras in type A using spectrum data of the Jucys-Murphy elements.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-18T08:57:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dirac cohomology",
      "symmetric group",
      "vogan morphism",
      "projective supermodules",
      "branching graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}