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Symmetric group
About: Symmetric group is a research topic. Over the lifetime, 7945 publications have been published within this topic receiving 134099 citations.
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Book•
28 Feb 1991
TL;DR: Group Representations.
Abstract: Group Representations.- Representations of the Symmetric Group.- Combinatorial Algorithms.- Symmetric Functions.- Applications and Generalizations.
1,055 citations
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01 Jan 2001
TL;DR: The first € price and the £ and $ price are net prices, subject to local VAT as mentioned in this paper, and they are subject to change without notice, including carriage charges, and are not guaranteed to be accurate.
Abstract: The first € price and the £ and $ price are net prices, subject to local VAT. Prices indicated with * include VAT for books; the €(D) includes 7% for Germany, the €(A) includes 10% for Austria. Prices indicated with ** include VAT for electronic products; 19% for Germany, 20% for Austria. All prices exclusive of carriage charges. Prices and other details are subject to change without notice. All errors and omissions excepted. B. Sagan The Symmetric Group
932 citations
Book•
12 Mar 2014
TL;DR: In this paper, the standard basis of the specht module is defined, and the branching theorem and branching theorem can be used to obtain irreducible representations of the symmetric group.
Abstract: Background from representation theory.- The symmetric group.- Diagrams, tableaux and tabloids.- Specht modules.- Examples.- The character table of .- The garnir relations.- The standard basis of the specht module.- The branching theorem.- p-regular partitions.- The irreducible representations of .- Composition factors.- Semistandard homomorphisms.- Young's rule.- Sequences.- The Littlewood-richardson rule.- A specht series for M?.- Hooks and skew-hooks.- The determinantal form.- The hook formula for dimensions.- The murnaghan-nakayama rule.- Binomial coefficients.- Some irreducible specht modules.- On the decomposition matrices of .- Young's orthogonal form.- Representations of the general linear group.
884 citations
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TL;DR: In this paper, the geometry of groups of Lie type was studied and the generalized Fitting subgroup was proposed. But it was not shown how to represent groups on groups and how to express finite groups.
Abstract: 1. Preliminary results 2. Permutation representations 3. Representation of groups on groups 4. Linear representations 5. Permutation groups 6. Extensions of groups and modules 7. Spaces with forms 8. p-groups 9. Change of field of a linear representation 10. Presentation of groups 11. The generalized Fitting subgroup 12. Linear representation of finite groups 13. Transfer and fusion 14. The geometry of groups of Lie type 15. Signalizer functors 16. Finite simple groups References List of symbols Index.
837 citations
01 Jan 1980
TL;DR: Polynomial Representations of GLn(K): The Schur algebra as mentioned in this paper, Weights and Characters., The modules D?K., The Carter-Lusztig modules V?,K., Representation theory of the symmetric group
Abstract: Polynomial Representations of GLn(K): The Schur algebra.- Weights and Characters.- The modules D?,K.- The Carter-Lusztig modules V?,K.- Representation theory of the symmetric group.
755 citations