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Applications of Frobenius Algebras to Representation Theory of Schur Algebras

✍ Scribed by L. Delvaux; E. Nauwelaerts

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
313 KB
Volume
199
Category
Article
ISSN
0021-8693

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✦ Synopsis

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 on class functions on Schur algebras.

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