SPEAKER: Malka Schaps
TITLE: Crossovers for covering groups of the symmetric and alternating groups
ABSTRACT This is joint work with Radha Kessar. We consider Morita equivalences among the faithful blocks of the covering groups S^~_n and A^~_n of the symmetric and alternating groups. Parity preserving equivalences obtained combinatorially were used by Kessar within each family of covering groups to prove Donovan's conjecture for these cases, i.e., that there are only a finite numbers of Morita equivalence classes of blocks for each defect group. We now show that the parity reversing involutions which cross over from one family to the other generate equally natural Morita equivalences, and that, in fact, the two families of blocks should be treated together.