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

Abstract

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.

78 pages, index of notation added, final version

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Cited by in corpus (16)

• Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras
• Graded decomposition numbers for cyclotomic Hecke algebras
• Graded Specht modules
• Quiver Schur algebras and q-Fock space
• 2-block Springer fibers: convolution algebras and coherent sheaves
• Current algebras and categorified quantum groups
• The degenerate analogue of Ariki's categorification theorem
• Graded cellular bases for the cyclotomic Khovanov-Lauda-Rouquier algebras of type A
• A diagrammatic categorification of the q-Schur algebra
• Seminormal forms and cyclotomic quiver Hecke algebras of type $A$
• A-infinity structures on the algebra of extensions of Verma modules in the parabolic category O
• Graded induction for Specht modules
• The Khovanov-Lauda 2-category and categorifications of a level two quantum sl(n) representation
• Colored sl(N) link homology via matrix factorizations
• Representations of Khovanov-Lauda-Rouquier Algebras and Combinatorics of Lyndon Words
• Derived equivalences and sl_2-categorifications for U_q(gl_n)