On Schur algebras and related algebras. II

DOI10.1016/0021-8693(87)90222-5zbMath0634.20019OpenAlexW1983455389MaRDI QIDQ1096722

Stephen Donkin

Publication date: 1987

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8693(87)90222-5

zbMATH Keywords

Weyl modulesblockssoclesSchur algebraSchur functorYoung moduledominant weightsfinite dimensional Lie algebraSpecht seriesNakayama's conjecturerepresentation theory of the symmetric groupsweights of projective indecomposables

Mathematics Subject Classification ID

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

Related Items (64)

On Schur algebras and related algebras. I ⋮ A generic algebra associated to certain Hecke algebras. ⋮ On Mullineux symbols ⋮ Invariant functions on matrices ⋮ Resolutions of \(B\) modules ⋮ Resolutions, homological dimensions, and extension of hook representations ⋮ On Schur algebras and related algebras. V: Some quasi-hereditary algebras of finite type ⋮ Ext spaces for general linear and symmetric groups ⋮ Vertices of Low-Dimensional Simple Modules for Symmetric Groups ⋮ Presenting generalized Schur algebras in types \(B\), \(C\), \(D\). ⋮ A criterion for quasi-hereditary, and an abstract straightening formula ⋮ Presenting Hecke endomorphism algebras by Hasse quivers with relations ⋮ Exact Borel subalgebras of quasi-hereditary algebras. I. (With an appendix by Leonard Scott) ⋮ A row removal theorem for the Ext¹ quiver of symmetric groups and Schur algebras ⋮ Polynomial representations, algebraic monoids, and Schur algebras of classical type ⋮ On cohomology of dual Specht modules ⋮ On some trivial source Specht modules ⋮ Polynomial representations and categorifications of Fock space ⋮ Ringel duality and derivatives of non-additive functors ⋮ Filtrations for q-Young modules ⋮ On Schur algebras and related algebras III: integral representations ⋮ Composition factors of tensor products of truncated symmetric powers. ⋮ On the conjugation action for quantum general linear groups ⋮ On Schur algebras and related algebras. VI: Some remarks on rational and classical Schur algebras. ⋮ Generalized Schur algebras ⋮ The period of periodic Young modules. ⋮ Cellular bases of generalised q-Schur algebras ⋮ A bideterminant basis for a reductive monoid ⋮ Straightening rule for an \(m^{\prime}\)-truncated polynomial ring ⋮ Truncated symmetric powers and modular representations of GL_n ⋮ Horizontal partitions and Kleshchev's algorithm ⋮ Cellularity of endomorphism algebras of Young permutation modules ⋮ A characterisation of blocks of finite type. ⋮ The normality of closures of conjugacy classes of matrices ⋮ A geometric Schur functor. ⋮ Schur algebras of Brauer algebras. II. ⋮ Some remarks on tilting modules, double centralisers and Lie modules ⋮ On Ext-quivers of blocks of weight two for symmetric groups ⋮ All quasihereditary algebras with a regular exact Borel subalgebra ⋮ On vertices of simple modules for symmetric groups of small degrees. ⋮ Combinatorics and the Schur algebra ⋮ Schur subalgebras and an application to the symmetric group ⋮ Modular symmetric functions and irreducible modular representations of general linear groups ⋮ The Brauer algebra and the symplectic Schur algebra ⋮ Invariants of several matrices ⋮ Brauer algebras, symplectic Schur algebras and Schur-Weyl duality ⋮ On \(p\)-Kostka numbers and Young modules. ⋮ Endomorphism algebras of some modules for Schur algebras and representation dimension. ⋮ Decomposition numbers for distant Weyl modules ⋮ Schur and weyl functors, II ⋮ The rational Schur algebra ⋮ Modular Schur Functions ⋮ Constructing quantized enveloping algebras via inverse limits of finite dimensional algebras ⋮ Presenting generalized 𝑞-Schur algebras ⋮ On the socle of Weyl modules ⋮ Tilting modules, symmetric functions, and the module structure of the free Lie algebra ⋮ The varieties for some Specht modules. ⋮ Extensions of symmetric tensors by alternating tensors ⋮ Multiplication formulas and isomorphism theorem of \({\imath}\)Schur superalgebras ⋮ Cellular algebras and quasi-hereditary algebras: a comparison ⋮ On the complexities of some simple modules of symmetric groups ⋮ On tilting modules for algebraic groups ⋮ Representation Theory of Reductive Normal Algebraic Monoids ⋮ Modular representations of the supergroup \(Q(n)\). I

Cites Work

• Rational representations of algebraic groups: Tensor products and filtrations
• On Schur algebras and related algebras. I
• Finite resolutions of modules for reductive algebraic groups
• Polynomial representations of \(GL_n\)
• On the modular representations of the general linear and symmetric groups
• Locally finite representations
• The representation theory of the symmetric groups
• Characteristic-free representation theory of the general linear group. II: Homological considerations
• Trivial source modules for symmetric groups
• Filtrations of cohomology modules for Chevalley groups
• The strong linkage principle.
• The Decomposition of Relation Modules: A Correction
• Bijections of p -Regular Partitions and p -Modular Irreducibles of the Symmetric Groups
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