Bernstein–Gelfand–Gelfand resolutions and the constructible t-structure

Abstract

We consider analogues of the Bernstein–Gelfand–Gelfand resolution in a highest weight category P♡. We prove the resulting category of complexes is a chain-level lift of the heart of the constructible t-structure on its bounded derived category P. In particular, an object admits a Bernstein-Gelfand-Gelfand resolution if and only if a certain Ext vanishing with costandard objects holds. These results appear to be new even for Category O.