Morit7a equivalences of cyclotomic Hecke algebras of type G(r, p, n)

We prove a Morita reduction theorem for the cyclotomic Hecke algebras ℋ_{r, p, n}(q, Q) of type G(r, p, n) with p > 1 and n ≧ 3. As a consequence, we show that computing the decomposition numbers of ℋ_{r, p, n}(Q) reduces to computing the p′-splittable decomposition numbers (see Definition 1.1) of the cyclotomic Hecke algebras ℋ_{r′, p′, n′}(Q′), where 1 ≦ r′ ≦ r, 1 ≦ n′ ≦ n, p′ | p and where the parameters Q′ are contained in a single (ε′, q)-orbit and ε′ is a primitive p′th root of unity.