The cyclotomic non-degenerate Hecke algebras of arbitrary Weyl groups

We construct Khovanov–Lauda–Rouquier-like generators for certain modified forms of non-degenerate affine Hecke algebras associated with arbitrary Weyl groups after localization. These generators yield non-graded KLR-like presentations of the modified algebras. As an application, we establish isomorphisms between direct sums of blocks of cyclotomic Hecke algebras of arbitrary Weyl groups and cyclotomic quotients of the resulting non-graded KLR-like algebras. We also explain how these isomorphisms identify the generalized weight-space decomposition of cyclotomic Hecke modules with the idempotent decomposition of modules over the KLR-like presentation.