Characteristic-free representation theory of the general linear group

DOI10.1016/0001-8708(85)90115-XzbMath0607.20021WikidataQ105519280 ScholiaQ105519280MaRDI QIDQ1085277

Publication date: 1985

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

Schur functions skew partition tensor products exterior powers polynomial representations Schur functors Pieri formulas Schur complex finitely generated free R- modules

Mathematics Subject Classification ID

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

Related Items (43)

On Schur algebras and related algebras. I ⋮ 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 ⋮ Aspects of characteristic-free representation theory of \(GL_ n\), and some applications to intertwining numbers ⋮ On the Ext groups between Weyl modules for \(\text{GL}_n\). ⋮ Algebraic stratification in representation categories ⋮ Skew modules for reductive groups ⋮ A remark on integral representations of \(GL_{{\mathbb{Z}}}(n)\) ⋮ On complexes relating the Jacobi-Trudy identity with the Bernstein- Gelfand-Gelfand resolution ⋮ 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. ⋮ Permutation resolutions for Specht modules. ⋮ Resolutions of determinantal ideals: \(t\)-minors of \((t+2)\times{} n\) matrices ⋮ Schur and Weyl functors ⋮ Skew Weyl modules for \(\text{GL}_n\) and degree reduction for Schur algebras ⋮ On some plethysms ⋮ The Decompositions of Schur Complexes ⋮ Schur modules, Weyl modules, and Capelli operators. ⋮ Diagrammatic categorification of the Chebyshev polynomials of the second kind ⋮ A note on the Poincaré resolution of the coordinate ring of the Grassmannian ⋮ Two formulae for exterior power operations on higher \(K\)-groups ⋮ A straightening algorithm for row-convex tableaux ⋮ Schur--De-Rham complex and its cohomology ⋮ Approaches to resolution of Weyl modules. ⋮ Computations and applications of some homological constants for polynomial representations of 𝐺𝐿_{𝑛} ⋮ Relating tensor structures on representations of general linear and symmetric groups ⋮ Invariants of \(\mathrm G_2\) and Spin(7) in positive characteristic ⋮ A Combinatorial Description of the Syzygies of Certain Weyl Modules ⋮ Intertwining numbers; The n-rowed shapes ⋮ Quantum multilinear algebra ⋮ The umbral symbolic method for supersymmetric tensors ⋮ A short proof of a theorem of M. Hashimoto ⋮ Presentations of Schur complexes attached to row convex shapes ⋮ Characteristic-free representation theory of the general linear group. II: Homological considerations ⋮ Characteristic-free resolutions of Weyl and Specht modules. ⋮ Homotopies for the Generalized Bar Complex Associated to Certain 3-Rowed Weyl Modules ⋮ On commutative algebra and characteristic-free representation theory ⋮ Compressed straight tableaux and a distributive lattice of representations ⋮ Exterior power operations on higher \(K\)-groups via binary complexes

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