{
  "id": "math/0608234",
  "version": "v3",
  "published": "2006-08-10T01:12:22.000Z",
  "updated": "2008-03-06T06:09:12.000Z",
  "title": "Parabolic category O, perverse sheaves on Grassmannians, Springer fibres and Khovanov homology",
  "authors": [
    "Catharina Stroppel"
  ],
  "comment": "39 pages, 9 figures, added a few remarks",
  "journal": "Compositio Math. 2008",
  "doi": "10.1112/S0010437X09004035",
  "categories": [
    "math.RT",
    "math.GT"
  ],
  "abstract": "For a fixed parabolic subalgebra p of gl(n,C) we prove that the centre of the principal block O(p) of the parabolic category O is naturally isomorphic to the cohomology ring of the corresponding Springer fibre. We give a diagrammatic description of O(p) for maximal parabolic p and give an explicit isomorphism to Braden's description of the category Perv_B(G(n,n)) of perverse sheaves on Grassmannians. As a consequence Khovanov's algebra H^n is realised as the endomorphism ring of some object from Perv_B(G(n,n)) which corresponds under localisation and the Riemann-Hilbert correspondence to a full projective-injective module in the corresponding category $O(p)$. From there one can deduce that Khovanov's tangle invariants are obtained from the more general functorial invariants involving category O by restriction.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2008-03-06T06:09:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16S99",
      "17B10",
      "14M15",
      "57M27",
      "20C30",
      "20G05",
      "14M17"
    ],
    "keywords": [
      "parabolic category",
      "perverse sheaves",
      "khovanov homology",
      "grassmannians",
      "general functorial invariants"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......8234S"
    }
  }
}