  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.
