RoCK blocks of double covers of symmetric groups and generalized Schur algebras

Abstract

We study blocks of the double covers of symmetric and alternating groups. The main result is a `local' description, up to Morita equivalence, of arbitrary defect RoCK blocks of these groups in terms of generalized Schur superalgebras corresponding to an explicit Brauer tree superalgebra. In view of the recent results on Brou\'e's Conjecture for these groups, our result provides a `local' description of an arbitrary block of the double covers of symmetric and alternating groups up to derived equivalence.