{
  "id": "1802.01974",
  "version": "v1",
  "published": "2018-02-06T14:47:11.000Z",
  "updated": "2018-02-06T14:47:11.000Z",
  "title": "Classification of $A_{q}(λ)$ modules by their Dirac cohomology for type $D$ and $\\mathfrak{sp}(2n,\\mathbb{R})$",
  "authors": [
    "Ana Prlić"
  ],
  "comment": "19 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $G$ be a connected real reductive group with maximal compact subgroup $K$ of the same rank as $G$. In the recent paper of Huang, Pand\\v{z}i\\'{c} and Vogan, it was shown that the admissible $\\Theta$-stable parabolic subalgebras $\\mathfrak{q}$ of $\\mathfrak{g}$ are in one-to-one correspodence with the faces of $W \\rho$ intersecting the $\\mathfrak{k}$--dominant Weyl chamber and that $A_{\\mathfrak{q}}(0)$--modules can be classified by their Dirac cohomology in geometric terms. They described in detail the cases when $\\mathfrak{g}_0$ is of type $A$, $B$, $F$ and $C$ except for $\\mathfrak{g}_0 = \\mathfrak{sp}(2n, \\mathbb{R})$. We will describe faces corresponding to $A_{\\mathfrak{q}}(0)$-modules for $\\mathfrak{g}_0 = \\mathfrak{sp}(2n, \\mathbb{R})$ and for $\\mathfrak{g}_0$ of type $D$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-06T14:47:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dirac cohomology",
      "classification",
      "maximal compact subgroup",
      "dominant weyl chamber",
      "geometric terms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}