{
  "id": "1712.04169",
  "version": "v1",
  "published": "2017-12-12T08:28:21.000Z",
  "updated": "2017-12-12T08:28:21.000Z",
  "title": "Dirac Index and associated cycles of Harish-Chandra modules",
  "authors": [
    "Salah Mehdi",
    "Pavle Pandzic",
    "David Vogan",
    "Roger Zierau"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $G_{\\mathbb{R}}$ be a simple real linear Lie group with maximal compact subgroup $K_{\\mathbb{R}}$ and assume that ${\\rm rank}(G_\\mathbb{R})={\\rm rank}(K_\\mathbb{R})$. For any representation $X$ of Gelfand-Kirillov dimension $\\frac{1}{2} {\\rm dim}(G_{\\mathbb{R}}/K_{\\mathbb{R}})$, we consider the polynomial on the dual of a compact Cartan subalgebra given by the dimension of the Dirac index of members of the coherent family containing $X$. Under a technical condition involving the Springer correspondence, we establish an explicit relationship between this polynomial and the multiplicities of the irreducible components occurring in the associated cycle of $X$. This relationship was conjectured in \\cite{MehdiPandzicVogan15}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-12T08:28:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E47"
    ],
    "keywords": [
      "dirac index",
      "associated cycle",
      "harish-chandra modules",
      "simple real linear lie group",
      "maximal compact subgroup"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}