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 |
Keywords:
dominant weights; finite dimensional Lie algebras; Schur algebras; representation theory of symmetric groups; Schur functorsReferences:
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