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Symmetric groups and quasi-hereditary algebras. (English) Zbl 0831.20013
Dlab, V. (ed.) et al., Finite dimensional algebras and related topics. Proceedings of the NATO Advanced Research Workshop on Representations of algebras and related topics. Ottawa, Canada, August 10-18, 1992. Dordrecht: Kluwer Academic Publishers. NATO ASI Ser., Ser. C, Math. Phys. Sci. 424, 123-161 (1994).
In Chapter 1 we discuss quasi-hereditary algebras. We include some results which were proved for algebraic groups or Schur algebras and which generalize to arbitrary quasi-hereditary algebras. In Chapters 2 and 3 we summarise results on $$K \Sigma_r$$-modules and $$S(n,r)$$- modules ($$\Sigma_r$$ the symmetric group, $$S(n,r)$$ the Schur algebras of $$\text{GL}_n$$) respectively. In Chapters 4 and 5 we prove the main results, and the last chapter contains the result on filtration multiplicities and decomposition numbers of 2-part partitions.
For the entire collection see [Zbl 0797.00008].

##### MSC:
 20C30 Representations of finite symmetric groups 20G05 Representation theory for linear algebraic groups 20C05 Group rings of finite groups and their modules (group-theoretic aspects) 16S34 Group rings 16G30 Representations of orders, lattices, algebras over commutative rings