Morita Equivalence for Blocks of the Schur Algebras

✍ Scribed by K. Erdmann; S. Martin; J. Scopes

• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 296 KB
• Volume: 168
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1994.1232

✦ Synopsis

In [8], Scopes verified the Donovan conjecture for blocks of the finite symmetric groups. Her main theorem ( 1.3 below) was proved by finding a sufficient condition for Morita equivalence between two blocks of the same weight. Since there is a close connection between representations of the symmetric groups and representations of the Schur algebras, it is natural to ask if Scopes' result has an analogue for Schur algebras. The purpose of this paper is to present such an analogue as a direct deduction from the original paper [8]. We prove our equivalence over 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 framework. 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.