Stanley's formula for characters of the symmetric group.

DOI10.1007/s00026-009-0038-5zbMath1234.20014arXivmath/0612090OpenAlexW2036804768MaRDI QIDQ659808

Valentin Féray

Publication date: 24 January 2012

Published in: Annals of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0612090

zbMATH Keywords

irreducible complex charactersrepresentations of symmetric groupsYoung diagramsJucys-Murphy elementspartitions of rectangular shapeshifted Schur functions

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Representations of finite symmetric groups (20C30)

Related Items (16)

Bijection between oriented maps and weighted non-oriented maps ⋮ Skew Howe duality and random rectangular Young tableaux ⋮ Shifted symmetric functions and multirectangular coordinates of Young diagrams ⋮ Polynomiality of shifted Plancherel averages and content evaluations ⋮ A simple model of trees for unicellular maps ⋮ Quantum mechanics of bipartite ribbon graphs: integrality, lattices and Kronecker coefficients ⋮ Bijection between trees in Stanley character formula and factorizations of a cycle ⋮ Enumerative combinatorics. Abstracts from the workshop held December 11--17, 2022 ⋮ Asymptotics of characters of symmetric groups related to Stanley character formula ⋮ Zonal polynomials via Stanley's coordinates and free cumulants ⋮ Bijective enumeration of some colored permutations given by the product of two long cycles ⋮ Quantum spectrum testing ⋮ Explicit combinatorial interpretation of Kerov character polynomials as numbers of permutation factorizations ⋮ Bijection between trees in Stanley character formula and factorizations of a cycle ⋮ Linear versus spin: representation theory of the symmetric groups ⋮ Quasi-symmetric functions as polynomial functions on Young diagrams

Cites Work

• Positivity results for Stanley's character polynomials
• A new construction of Young's seminormal representation of the symmetric groups
• Irreducible symmetric group characters of rectangular shape.
• Symmetric polynomials and the center of the symmetric group ring
• Quantum immanants and higher Capelli identities
• Stanley's character polynomials and coloured factorisations in the symmetric group
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