Stroppel, C. (2009) Parabolic category O, perverse sheaves on Grassmannians, Springer fibres and Khovanov homology. Compositio Mathematica, 145(04), pp. 954-992. (doi: 10.1112/S0010437X09004035)
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Publisher's URL: http://dx.doi.org/10.1112/S0010437X09004035
Abstract
For a fixed parabolic subalgebra p of gl(n, C) we prove that the centre of the principal block O-0(p) of the parabolic category 0 is naturally isomorphic to the cohomology ring H*(B-p) of the corresponding Springer fibre. We give a. diagrammatic description of O-0(p) for maximal parabolic p and give an explicit isomorphism to Braden's description of the category Perv(B)(G(k,,n)) of Schubert-constructible 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-0(p). From there one can deduce that Khovanov's tangle invariants are obtained from the more general functorial invariants in [C. Stroppel, Catgorification of the Temperley Lieb category, tangles, and cobordisms via projective functors, Duke Math. J. 126(3) (2005), 547-596] by restriction.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Stroppel, Dr Catharina |
| Authors: | Stroppel, C. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Compositio Mathematica |
| ISSN: | 0010-437X |
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