Characteristic-free bases and BGG resolutions of unitary simple modules for quiver Hecke and Cherednik algebras

Abstract

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.

New section added proving that the Mullineux map preserves the set of unitary simples and explicitly constructing the Mullineux isomorphisms between these simples