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.