DG-enhanced Hecke and KLR algebras
Résumé
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.
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