We find that the cyclotomic KLR algebra of type A and blocks of the cyclotomic (degenerate) affine Hecke algebra of a symmetric group can be realized as the same quotient of an algebra. This can be seen as a re-proof of the Brundan-Kleshchev-Rouquier isomorphism. Our approach is based on the computations in suitable localization of the affine Hecke algebras by following Rouquier and our technique is based on Brundan and Kleshchev's original proof.
Kong et al. (2026) studied this question.