Characteristic-free representation theory of the general linear group. II: Homological considerations

DOI10.1016/0001-8708(88)90027-8zbMath0681.20028OpenAlexW1989660473MaRDI QIDQ1823318

David A. Buchsbaum, Kaan Akin

Publication date: 1988

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0001-8708(88)90027-8

zbMATH Keywords

partitionsfree modulesymmetric groupSchur moduleWeyl moduleexterior powersSchur algebradivided power algebraalgebra of \(\Gamma\)-endomorphismssums of tensor products of divided powers

Mathematics Subject Classification ID

Representations of finite symmetric groups (20C30) Representation theory for linear algebraic groups (20G05) Cohomology theory for linear algebraic groups (20G10)

Related Items (40)

On Schur algebras and related algebras. I ⋮ Matrix invariants over an infinite field of finite characteristic ⋮ Characteristic-free representation theory of the general linear group ⋮ Finite resolutions of modules for reductive algebraic groups ⋮ THE DIRICHLET HOPF ALGEBRA OF ARITHMETICS ⋮ A characteristic-free example of a Lascoux resolution, and letter-place methods for intertwining numbers. ⋮ Resolutions, homological dimensions, and extension of hook representations ⋮ On Schur algebras and related algebras. II ⋮ Aspects of characteristic-free representation theory of \(GL_ n\), and some applications to intertwining numbers ⋮ On the Ext groups between Weyl modules for \(\text{GL}_n\). ⋮ Addendum: Specht modules for column-convex diagrams: Characteristic-free results for Weyl modules ⋮ Skew modules for reductive groups ⋮ Ringel duality and derivatives of non-additive functors ⋮ Permanents, Doty coalgebras and dominant dimension of Schur algebras ⋮ Homotopies for resolutions of skew-hook shapes. ⋮ Permutation resolutions for Specht modules of Hecke algebras. ⋮ On homomorphisms into Weyl modules corresponding to partitions with two parts ⋮ Permutation resolutions for Specht modules. ⋮ Generic and \(q\)-rational representation theory ⋮ Skew Weyl modules for \(\text{GL}_n\) and degree reduction for Schur algebras ⋮ On some plethysms ⋮ On complexes relating the Jacobi-Trudi identity with the Bernstein- Gelfand-Gelfand resolution. II ⋮ Semi-invariants of quivers as determinants ⋮ On the Littlewood-Richardson rule for almost skew-shapes ⋮ Approaches to resolution of Weyl modules. ⋮ Relating tensor structures on representations of general linear and symmetric groups ⋮ A Combinatorial Description of the Syzygies of Certain Weyl Modules ⋮ Intertwining numbers; The n-rowed shapes ⋮ On homomorphisms involving a hook Weyl module ⋮ Quantum multilinear algebra ⋮ Polynomial representations of \(\mathrm{GL}(n)\) and Schur-Weyl duality. ⋮ Integral \(\mathrm{Ext}^2\) between hook Weyl modules ⋮ Extensions of symmetric tensors by alternating tensors ⋮ Characteristic-free resolutions of Weyl and Specht modules. ⋮ On extensions of hook Weyl modules ⋮ Homotopies for the Generalized Bar Complex Associated to Certain 3-Rowed Weyl Modules ⋮ Koszul, Ringel and Serre duality for strict polynomial functors ⋮ On commutative algebra and characteristic-free representation theory ⋮ On tilting modules for algebraic groups ⋮ Exterior power operations on higher \(K\)-groups via binary complexes

Cites Work

• Unnamed Item
• \(\lambda\)-rings and the representation theory of the symmetric group
• Characteristic-free representation theory of the general linear group
• Polynomial representations of \(GL_n\)
• Schur functors and Schur complexes
• On the modular representations of the general linear and symmetric groups
• On homomorphisms between Weyl modules and Specht modules

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