Applications of Frobenius algebras to representation theory of schur algebras

Abstract

A Schur algebra is a subalgebra of the group algebra RG associated to a partition of G, where G is a finite group and R is a commutative ring. For two classes of Schur algebras we study the relationship between indecomposable modules over the Schur algebra and over RG, but we discuss this problem in a more general context. Further we develop a character theory for Schur algebras; in particular, we express primitive central idempotents in terms of trace functions and we derive orthogonality relations for trace functions. These results are also presented in a more general context, namely for Frobenius algebras over rings. Moreover. we focus an class functions on Schur algebras. (C) 1998 Academic Press.