DG-enhanced Hecke and KLR algebras

Dos Santos Santana Forte Vaz, Pedro [UCL] et al.

We construct DG-enhanced versions of the degenerate affine Hecke algebra and of the affine q-Hecke algebra. We extend Brundan-Kleshchev and Rouquier's isomorphism and prove that after completion DG-enhanced versions of Hecke algebras are isomorphic to completed DG-enhanced versions of KLR algebras for suitably defined quivers. As a byproduct, we deduce that these DG-algebras have homologies concentrated in degree zero. These homologies are isomorphic respectively to the degenerate cyclotomic Hecke algebra and the cyclotomic q-Hecke algebra.