On Schur algebras and related algebras. I (Q1084507)

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.