Content evaluation and class symmetric functions

DOI10.1016/j.aim.2003.09.010zbMath1059.05104OpenAlexW2026829591MaRDI QIDQ1886578

Alain Goupil, Gilles Schaeffer, Sylvie Corteel

Publication date: 18 November 2004

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

Full work available at URL: https://doi.org/10.1016/j.aim.2003.09.010

zbMATH Keywords

Hecke algebrasconjugacy classessymmetric groupstableauxsymmetric functionscontentshift-symmetric functions

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Combinatorial aspects of representation theory (05E10) Representations of finite symmetric groups (20C30)

Related Items (27)

Integrality in the Matching-Jack conjecture and the Farahat-Higman algebra ⋮ Positivity results for Stanley's character polynomials ⋮ Polynomiality of shifted Plancherel averages and content evaluations ⋮ Asymptotically trivial linear homogeneous partition inequalities ⋮ On complete functions in Jucys-Murphy elements ⋮ BPS states, conserved charges and centres of symmetric group algebras ⋮ Stable centres of wreath products ⋮ Quantum mechanics of bipartite ribbon graphs: integrality, lattices and Kronecker coefficients ⋮ The perfect matching association scheme ⋮ A generalized dominance ordering for 1/2-BPS states ⋮ Combinatoric topological string theories and group theory algorithms ⋮ Integrality in the matching-Jack conjecture and the Farahat-Higman algebra ⋮ The quantum detection of projectors in finite-dimensional algebras and holography ⋮ Stable centres of Iwahori-Hecke algebras of type A ⋮ Quantum spectrum testing ⋮ Jack characters and enumeration of maps ⋮ Asymptotics of the number of standard Young tableaux of skew shape ⋮ An explicit formula for the characters of the symmetric group. ⋮ Explicit combinatorial interpretation of Kerov character polynomials as numbers of permutation factorizations ⋮ Katriel's operators for products of conjugacy classes of \(\mathfrak S_n\) ⋮ On the Okounkov-Olshanski formula for standard tableaux of skew shapes ⋮ Spectra of random linear combinations of matrices defined via representations and Coxeter generators of the symmetric group ⋮ Asymptotics for skew standard Young tableaux via bounds for characters ⋮ Explicitation of characters of the symmetric group. ⋮ An explicit form for Kerov's character polynomials ⋮ Quasi-symmetric functions as polynomial functions on Young diagrams ⋮ 2D Toda \(\tau\)-functions as combinatorial generating functions

Cites Work

• A new approach to representation theory of symmetric groups
• The idempotents of the symmetric group and Nakayama's conjecture
• A Frobenius formula for the characters of the Hecke algebras
• A variational problem for random Young tableaux
• Representations of symmetric groups and free probability
• Symmetric functions and Macdonald's result for top connexion coefficients in the symmetric group
• Shifted Jack polynomials, binomial formula, and applications
• Symmetric polynomials and the center of the symmetric group ring
• Explicit expressions for the central characters of the symmetric group
• The centres of symmetric group rings
• Some useful results concerning the representation theory of the symmetric group
• The Center of ℤ[ S n+1 is the Set of Symmetric Polynomials in n Commuting Transposition-Sums]
• Representation-free evaluation of the eigenvalues of the class-sums of the symmetric group
• Some Characters of the Symmetric Group
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