On Schur algebras and related algebras. I
type: Item
instance of: scholarly article
title: On Schur algebras and related algebras. I
zbMATH Open document ID: 0606.20038
DOI: 10.1016/0021-8693(86)90218-8
author: Stephen Donkin
published in: Journal of Algebra
publication date: 1986-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 20G20
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 17B10
Mathematics Subject Classification ID: 20C30
Mathematics Subject Classification ID: 20F40
Mathematics Subject Classification ID: 20G10
zbMATH DE Number: 3979363
zbMATH Keywords: dominant weights
zbMATH Keywords: finite dimensional Lie algebras
zbMATH Keywords: Schur algebras
zbMATH Keywords: representation theory of symmetric groups
zbMATH Keywords: Schur functors
MaRDI profile type: Publication
full work available at URL: 0021-8693(86)90218-8
OpenAlex ID: W4210444050
cites work: Schur functors and Schur complexes
cites work: Characteristic-free representation theory of the general linear group
cites work: Characteristic-free representation theory of the general linear group. II: Homological considerations
cites work: Q5594655
cites work: On the modular representations of the general linear and symmetric groups
cites work: Sur certains groupes simples
cites work: Cohomology, hyperalgebras, and representations
cites work: Rational and generic cohomology
cites work: Hopf Complements and Injective Comodules for Algebraic Groups
cites work: A filtration for rational modules
cites work: Rational representations of algebraic groups: Tensor products and filtrations
cites work: On Schur algebras and related algebras. II
cites work: Skew modules for reductive groups
cites work: Cohomology of Lie Algebras and Algebraic Groups
cites work: Q4732617
cites work: Locally finite representations
cites work: Polynomial representations of \(GL_n\)
cites work: Q3728210
cites work: Sur quelques points d'algèbre homologique
cites work: Q3313974
cites work: Cohomology of algebraic linear groups
cites work: Trivial source modules for symmetric groups
cites work: Darstellungen halbeinfacher Gruppen und kontravariante Formen.
cites work: Darstellungen halbeinfacher Gruppen und ihrer Frobenius-Kerne.
cites work: Good Bimodule Filtrations for Coordinate Rings
cites work: Q5590089
description: scientific article; zbMATH DE number 3979363