Multivariate polynomials, standard tableaux, and representations of symmetric groups

DOI10.1016/S0747-7171(08)80117-4zbMath0733.20005OpenAlexW1980790540MaRDI QIDQ810138

Michael Clausen

Publication date: 1991

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0747-7171(08)80117-4

zbMATH Keywords

algorithmsfinite permutation groupssimple modulesLittlewood-Richardson rulemonomial basesstandard tableauxCapelli operatorsgeneralized Laplace expansionsLaplace dualityRobinson-Schensted-Schützenberger-Knuth correspondenceskew modulesSpecht series

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Representations of finite symmetric groups (20C30) Vector and tensor algebra, theory of invariants (15A72) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Group rings of finite groups and their modules (group-theoretic aspects) (20C05)

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A unified FFT-based approach to maximum assignment problems related to transitive finite group actions, Modular irreducible representations of the symmetric group as linear codes., Relations between the Clausen and Kazhdan-Lusztig representations of the symmetric group., Tableau algorithms defined naturally for pictures, Symmetrizers for Schur superalgebras, Bitableaux and zero sets of dual canonical basis elements, Combinatorics and the Schur algebra, A note on bideterminants for Schur superalgebras

Cites Work

• Dominance orders, Capelli operators, and straightening of bideterminants
• Symplectic standard tableaux
• Letter place algebras and a characteristic-free approach to the representation theory of the general linear and symmetric groups. I
• Traceless tensors and the symmetric group
• Young diagrams and determinantal varieties
• Invarianten unipotenter Gruppen
• Young diagrams and ideals of Pfaffians
• The symplectic group and determinants
• An algorithm for the Rota straightening formula
• Polynomial representations of \(GL_n\)
• Letter place algebras and a characteristic-free approach to the representation theory of the general linear and symmetric groups. II
• A generalization of the Littlewood-Richardson rule and the Robinson- Schensted-Knuth correspondence
• On the variety of complexes
• On the modular representations of the general linear and symmetric groups
• A characteristic free approach to invariant theory
• A characteristic-free approach to the representation theory of \(\mathfrak S_n\)
• Skew-symmetric invariant theory
• Invariant theory, Young bitableaux, and combinatorics
• Specht series for skew representations of symmetric groups
• Permutations, matrices, and generalized Young tableaux
• Determinantal ideals, identities, and the Wronskian
• Longest Increasing and Decreasing Subsequences
• Symmetrized skew determinants
• On the Foundations of Combinatorial Theory: IX Combinatorial Methods in Invariant Theory
• Induced representations of reductive ${\germ p}$-adic groups. II. On irreducible representations of ${\rm GL}(n)$
• On the differential invariants of a linear ordinary differential equation
• Quelques remarques sur une Construction de Schensted.
• Theory and Application of Plane Partitions: Part 1
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