In mathematics, Schur algebras, named after Issai Schur, are certain finite-dimensional algebras closely associated with Schur–Weyl duality between general linear and symmetric groups. They are used to relate the representation theories of those two groups. Their use was promoted by the influential monograph of J. A. Green first published in 1980.[1] The name "Schur algebra" is due to Green. In the modular case (over infinite fields of positive characteristic) Schur algebras were used by Gordon James and Karin Erdmann to show that the (still open) problems of computing decomposition numbers for general linear groups and symmetric groups are actually equivalent.[2] Schur algebras were used by Friedlander and Suslin to prove finite generation of cohomology of finite group schemes.[3]
^J. A. Green, Polynomial Representations of GLn, Springer Lecture Notes 830, Springer-Verlag 1980. MR2349209, ISBN 978-3-540-46944-5, ISBN 3-540-46944-3
^Karin Erdmann, Decomposition numbers for symmetric groups and composition factors of Weyl modules. Journal of Algebra 180 (1996), 316–320. doi:10.1006/jabr.1996.0067 MR1375581
^Eric Friedlander and Andrei Suslin, Cohomology of finite group schemes over a field. Inventiones Mathematicae 127 (1997), 209--270. MR1427618 doi:10.1007/s002220050119
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after Issai Schur: List of things named after Issai SchurSchuralgebraSchur complement Schur index Schur indicator Schur multiplier Schur orthogonality...
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