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On Schur algebras and related algebras. I. (English) Zbl 0606.20038
The author defines an $$R$$-algebra $$S_ R(\pi)$$ for each finite saturated set $$\pi$$ of dominant weights of a semisimple, complex, finite dimensional Lie algebra $$\mathfrak g$$. When $$\mathfrak g=\mathfrak{sl}_ n(C)$$, then if $$\pi$$ is chosen carefully, the construction generalizes that of the Schur algebras. The author obtains results on the representation theory of the symmetric groups by applying the Schur functor.
Reviewer: J.H.Lindsey, II

MSC:
 20G20 Linear algebraic groups over the reals, the complexes, the quaternions 20G05 Representation theory for linear algebraic groups 17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) 20C30 Representations of finite symmetric groups 20F40 Associated Lie structures for groups 20G10 Cohomology theory for linear algebraic groups
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