Morita equivalences between cyclotomic KLR algebras in types C∞ and A∞

Abstract We prove that level one cyclotomic Khovanov–Lauda–Rouquier (KLR) algebras in type are graded Morita equivalent to level two cyclotomic KLR algebras in type . We hence deduce the graded decomposition numbers and full submodule structures of all level one cyclotomic KLR algebras in type .