MORITA EQUIVALENCE FOR BLOCKS OF THE SCHUR ALGEBRAS

In [8], Scopes verified the Donovan conjecture for blocks of the finit e symmetric groups. Her main theorem (1.3 below) was proved by finding a sufficient condition for Morita equivalence between two blocks of t he same weight. Since there is a close connection between representati ons of the symmetric groups and representations of the Schur algebras, it is natural to ask if Scopes' result has an analogue for Schur alge bras. The purpose of this paper is to present such an analogue as a di rect deduction from the original paper [8]. We prove our equivalence o ver a complete discrete valuation ring, thus in the process obtaining more precise information about Young modules. However, our main result on Morita equivalence could be proved without recourse to this framew ork. We remark that Donkin [2, Section 5] has given a different proof of both Scopes' result and our Theorem 2.2, though he too makes use of the combinatorial setup of [8]. (C) 1994 Academic Press, Inc.