Ribbon blocks for centraliser algebras of symmetric groups

Suppose $l,m$ are natural numbers with

, and $F$ a field of characteristic p, and let $C_{l,m}^F$ denote the centraliser of the group algebra $F{S}_l$ inside $F{S}_m$. Ellers and Murray give a conjectured classification of the blocks of $C_{l,m}^F$, in terms of the p-blocks of $S_l$ and $S_m$. We prove this conjecture for a family of blocks that we call ribbon blocks and belt blocks. These are the blocks containing Specht modules labelled by skew-partitions having no repeated entries in their p-content.