{
  "id": "0909.1860",
  "version": "v4",
  "published": "2009-09-10T02:29:47.000Z",
  "updated": "2011-01-27T06:34:00.000Z",
  "title": "Singular blocks of parabolic category O and finite W-algebras",
  "authors": [
    "Ben Webster"
  ],
  "comment": "12 pages; v2 and v3: minor corrections suggested by referee; statement of some results changed; v4: additional material added on connection to Slodowy slices and rewrite of introduction",
  "doi": "10.1016/j.jpaa.2011.03.020",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "We show that each integral infinitesimal block of parabolic category O (including singular ones) for a semi-simple Lie algebra can be realized as a full subcategory of a \"thick\" category O over a finite W-algebra for the same Lie algebra. The nilpotent used to construct this finite W-algebra is determined by the central character of the block, and the subcategory taken is that killed by a two-sided ideal depending on the original parabolic. The equivalences in question are induced by those of Milicic-Soergel and Losev. We also give a proof of a result of some independent interest: the singular blocks of parabolic category O can be geometrically realized as \"partial Whittaker sheaves\" on partial flag varieties.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2011-01-27T06:34:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10",
      "81R10"
    ],
    "keywords": [
      "parabolic category",
      "finite w-algebra",
      "singular blocks",
      "partial flag varieties",
      "semi-simple lie algebra"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0909.1860W"
    }
  }
}