Ozsvath-Szabo bordered algebras and subquotients of category O

We show that Ozsvath-Szabo'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 Ozsvath-Szabo 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-circle times n for U-q(gl(1 vertical bar 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 Ozsvath-Szabo's algebra lifting various bases of V-circle times n, and bimodules over Ozsvath-Szabo's algebra categorifying the action of the quantum group element F and its dual on V (circle times n). (c) 2020 Elsevier Inc. All rights reserved.