# Parabolic category O, perverse sheaves on Grassmannians, Springer fibres and Khovanov homology

@article{Stroppel2009ParabolicCO,
title={Parabolic category O, perverse sheaves on Grassmannians, Springer fibres and Khovanov homology},
author={C. Stroppel},
journal={Compositio Mathematica},
year={2009},
volume={145},
pages={954 - 992}
}
• C. Stroppel
• Published 2009
• Mathematics
• Compositio Mathematica
Abstract For a fixed parabolic subalgebra 𝔭 of $\mathfrak {gl}(n,\mathbb {C})$ we prove that the centre of the principal block 𝒪0𝔭 of the parabolic category 𝒪 is naturally isomorphic to the cohomology ring H*(ℬ𝔭) of the corresponding Springer fibre. We give a diagrammatic description of 𝒪0𝔭 for maximal parabolic 𝔭 and give an explicit isomorphism to Braden’s description of the category PervB(G(k,n)) of Schubert-constructible perverse sheaves on Grassmannians. As a consequence Khovanov’s… Expand
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