Letter place algebras and a characteristic-free approach to the representation theory of the general linear and symmetric groups. I

DOI10.1016/S0001-8708(79)80004-3zbMath0425.20011MaRDI QIDQ1135357

Michael Clausen

Publication date: 1979

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

zbMATH Keywords

Weyl modulescharacteristic-free approach to the representation theory of the general linear groupsirreducible modules for symmetric groupsletter place algebrassymmetrized bideterminants

Mathematics Subject Classification ID

Representations of finite symmetric groups (20C30)

Related Items (21)

Modular irreducible representations of the symmetric group as linear codes. ⋮ Representations of finite groups ⋮ The Littlewood-Richardson rule for Coschur modules ⋮ Permanents and determinants with generic noncommuting entries ⋮ A computer oriented algorithm for the determination of the dimension and character of a modular irreducible SL(n,K)-module ⋮ Permanents, Doty coalgebras and dominant dimension of Schur algebras ⋮ Letter place algebras and a characteristic-free approach to the representation theory of the general linear and symmetric groups. II ⋮ Symmetrized skew determinants ⋮ Non-crossing tableaux ⋮ Remark on the branching theorem and supersymmetric algebras ⋮ Schur and Weyl functors ⋮ Skew Weyl modules for \(\text{GL}_n\) and degree reduction for Schur algebras ⋮ Schur modules, Weyl modules, and Capelli operators. ⋮ Combinatorics and the Schur algebra ⋮ Schur and weyl functors, II ⋮ Bases for spaces of highest weight vectors in arbitrary characteristic ⋮ Intertwining numbers; The n-rowed shapes ⋮ The umbral symbolic method for supersymmetric tensors ⋮ Trivial source modules for symmetric groups ⋮ A straightening formula for bipermanents ⋮ Multivariate polynomials, standard tableaux, and representations of symmetric groups

Cites Work

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• On the modular representations of the general linear and symmetric groups
• Specht modules and symmetric groups
• A characteristic-free approach to the representation theory of \(\mathfrak S_n\)
• Invariant theory, Young bitableaux, and combinatorics
• The representation theory of the symmetric groups
• Ordering the partition characters of the symmetric group
• Group characters and nonnegative integral matrices
• On the decomposition of modular tensors. I, II
• On the Foundations of Combinatorial Theory: IX Combinatorial Methods in Invariant Theory
• Modular Representations of Finite Groups of Lie Type
• The Irreducible Representations of the Symmetric Groups

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