Zonal polynomials via Stanley's coordinates and free cumulants

DOI10.1016/j.jalgebra.2011.03.008zbMath1235.05145arXiv1005.0316OpenAlexW2082621809MaRDI QIDQ653391

Valentin Féray, Piotr Śniady

Publication date: 19 December 2011

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1005.0316

zbMATH Keywords

symmetric functionszonal polynomialsfree cumulantsalgebraic combinatoricsmaps on non-oriented surfaces

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05)

Related Items (10)

Bijection between oriented maps and weighted non-oriented maps ⋮ Gaussian fluctuations of Young diagrams and structure constants of Jack characters ⋮ The Horn problem for real symmetric and quaternionic self-dual matrices ⋮ Cyclic Inclusion-Exclusion ⋮ A spin analogue of Kerov polynomials ⋮ Shifted symmetric functions and multirectangular coordinates of Young diagrams ⋮ Moments of the eigenvalue densities and of the secular coefficients ofβ-ensembles ⋮ Enumerative combinatorics. Abstracts from the workshop held December 11--17, 2022 ⋮ Asymptotics of Jack characters ⋮ Linear versus spin: representation theory of the symmetric groups

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Asymptotics of characters of symmetric groups related to Stanley character formula
• Stanley's formula for characters of the symmetric group.
• Zonal polynomials of the real positive definite symmetric matrices
• Combinatorial interpretation and positivity of Kerov's character polynomials
• Explicit combinatorial interpretation of Kerov character polynomials as numbers of permutation factorizations
• Jack polynomials and free cumulants
• Jack symmetric functions and some combinatorial properties of Young symmetrizers
• Representations of symmetric groups and free probability
• Shifted Jack polynomials, binomial formula, and applications
• The Selberg-Jack symmetric functions
• Irreducible symmetric group characters of rectangular shape.
• Some combinatorial properties of Jack symmetric functions
• Upper bound on the characters of the symmetric groups for balanced Young diagrams and a generalized Frobenius formula.
• Gaussian fluctuations of characters of symmetric groups and of Young diagrams
• A positivity conjecture for Jack polynomials
• Maps in Locally Orientable Surfaces, the Double Coset Algebra, and Zonal Polynomials
• The Distribution of the Latent Roots of the Covariance Matrix
• The algebra of conjugacy classes in symmetric groups, and partial permutations

This page was built for publication: Zonal polynomials via Stanley's coordinates and free cumulants