Abstract
We show that Ozsváth–Szabó's bordered algebra used to efficiently compute knot Floer homology is a graded flat deformation of the regular block of a q-presentable quotient of parabolic category O. We identify the endomorphism algebra of a minimal projective generator for this block with an explicit quotient of the Ozsváth–Szabó algebra using Sartori's diagrammatic formulation of the endomorphism algebra. Both of these algebras give rise to categorifications of tensor products of the vector representation V⊗n for Uq(gl(1|1)). Our isomorphism allows us to transport a number of constructions between these two algebras, leading to a new (fully) diagrammatic reinterpretation of Sartori's algebra, new modules over Ozsváth–Szabó's algebra lifting various bases of V⊗n, and bimodules over Ozsváth–Szabó's algebra categorifying the action of the quantum group element F and its dual on V⊗n.
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