Highest weight categories arising from Khovanov's diagram algebra III: category O

Understand

We prove that integral blocks of parabolic category O associated to the subalgebra gl(m) x gl(n) of gl(m+n) are Morita equivalent to quasi-hereditary covers of generalised Khovanov algebras.

• Although this result is in principle known, the existing proof is quite indirect, going via perverse sheaves on Grassmannians.
• Our new approach is completely algebraic, exploiting Schur-Weyl duality for higher levels.
• As a by-product we get a concrete combinatorial construction of 2-Kac-Moody representations in the sense of Rouquier corresponding to level two weights in finite type A.