Spin block inclusions

In this paper we classify all block equalities and all nontrivial block inclusions for spin blocks of the double covers of the symmetric groups at different odd primes. More generally, we describe for an odd integer s > 1 explicitly when an s̄-block of bar partitions is contained in a t̄-block of bar partitions, for t > 1 an odd integer or t = 4. The question of block equality leads to the study of (s̄, t̄)-cores. In the case of primes they label spin characters which are of defect 0 for different primes and therefore represent a block equality. We enumerate these cores and show that there is a unique maximal one.