  We construct characteristic-free bases and BGG resolutions of unitary simple
modules of quiver Hecke algebras and Cherednik algebras. We hence solve and
vastly generalise Berkesch-Griffeth-Sam's conjecture, calculate the
Castelnuovo-Mumford regularity of ideals of of certain highly symmetric linear
subspace arrangements, and compute Dirac homology of Cherednik algebras.
