The representation theory of the symmetric group
01 Jan 1984-
TL;DR: In this paper, the authors propose a representation theory of symmetric groups and their young subgroups, which is based on the notion of irreducible matrix representations of groups.
Abstract: 1. Symmetric groups and their young subgroups 2. Ordinary irreducible representations and characters of symmetric and alternating groups 3. Ordinary irreducible matrix representations of symmetric groups 4. Representations of wreath products 5. Applications to combinatories and representation theory 6. Modular representations 7. Representation theory of Sn over an arbitrary field 8. Representations of general linear groups Appendices Index.
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671 citations
TL;DR: In this paper, a simple one-person card game, called patience sorting, is described and its analysis leads to a broad circle of ideas linking Young tableaux with the longest increasing subsequence of a random permutation via the Schensted correspondence.
Abstract: We describe a simple one-person card game, patience sorting. Its analysis leads to a broad circle of ideas linking Young tableaux with the longest increasing subsequence of a random permutation via the Schensted correspondence. A recent highlight of this area is the work of Baik-Deift-Johansson which yields limiting probability laws via hard analysis of Toeplitz determinants.
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Book•
01 Jan 1979
TL;DR: In this paper, the characters of GLn over a finite field and the Hecke ring of GLs over finite fields have been investigated and shown to be symmetric functions with two parameters.
Abstract: I. Symmetric functions II. Hall polynomials III. HallLittlewood symmetric functions IV. The characters of GLn over a finite field V. The Hecke ring of GLn over a finite field VI. Symmetric functions with two parameters VII. Zonal polynomials
8,730 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
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
Additional excerpts
...Over F2 there is an isomorphism S(5,1,1) ∼= S(5,2) ⊕ S(7)....
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...Conversely since t = t?, we clearly have {t}k = {t?}k for all k ∈ C(t) ∩ C(t) = 〈(5, 8), (6, 9), (7, 10)〉....
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Journal Article•
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