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

References in corpus (5)

• Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras
• The many graded cellular bases of Hecke algebras
• Relating Signed Kazhdan-Lusztig Polynomials and Classical Kazhdan-Lusztig Polynomials
• Castelnuovo-Mumford regularity and arithmetic Cohen-Macaulayness of complete bipartite subspace arrangements
• Modular decomposition numbers of cyclotomic Hecke and diagrammatic Cherednik algebras: A path theoretic approach

Cited by in corpus (3)

• The many graded cellular bases of Hecke algebras
• A computer algorithm for the BGG resolution
• Modular decomposition numbers of cyclotomic Hecke and diagrammatic Cherednik algebras: A path theoretic approach