Morita 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). As a consequence, we show that computing the decomposition numbers of H_{r,p,n}(Q) reduces to computing the p’-splittable decomposition numbers of the cyclotomic Hecke algebras H_{r’,p’,n’}(Q’), where $1\le r^{\mathrm{\prime }}\le r$, $1\le n^{\mathrm{\prime }}\le n$, $p^{\mathrm{\prime }}\mid p$ and where the parameters Q’ are contained in a single $(ϵ,q)$-orbit and $ϵ$ is a primitive p’th root of unity.