Asymptotics of characters of symmetric groups related to Stanley character formula

DOI10.4007/annals.2011.173.2.6zbMath1229.05276arXivmath/0701051OpenAlexW3102179705MaRDI QIDQ640756

Valentin Féray, Piotr Śniady

Publication date: 20 October 2011

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0701051

zbMATH Keywords

representations of symmetric groupsasymptotic representation theoryfactorizations of permutations

Mathematics Subject Classification ID

Related Items (26)

Commutators of random matrices from the unitary and orthogonal groups ⋮ Asymptotics for the number of standard tableaux of skew shape and for weighted lozenge tilings ⋮ Bijection between oriented maps and weighted non-oriented maps ⋮ Combinatorial interpretation and positivity of Kerov's character polynomials ⋮ Skew Howe duality and random rectangular Young tableaux ⋮ A spin analogue of Kerov polynomials ⋮ Shifted symmetric functions and multirectangular coordinates of Young diagrams ⋮ Character estimates for finite simple groups and applications ⋮ Macdonald polynomials and chromatic quasisymmetric functions ⋮ The quantum detection of projectors in finite-dimensional algebras and holography ⋮ Asymptotics of characters of symmetric groups: structure of Kerov character polynomials ⋮ Random matrices associated to Young diagrams ⋮ Limit shapes of evacuation and jeu de taquin paths in random square tableaux ⋮ Symmetric group representations and \(\mathbb{Z}\) ⋮ Second class particles and limit shapes of evacuation and sliding paths for random tableaux. ⋮ Zonal polynomials via Stanley's coordinates and free cumulants ⋮ Jack characters and enumeration of maps ⋮ Asymptotics of the number of standard Young tableaux of skew shape ⋮ Free probability theory. And its avatars in representation theory, random matrices, and operator algebras; also featuring: non-commutative distributions ⋮ Asymptotics of Jack characters ⋮ Explicit combinatorial interpretation of Kerov character polynomials as numbers of permutation factorizations ⋮ Partial sum of matrix entries of representations of the symmetric group and its asymptotics ⋮ Linear versus spin: representation theory of the symmetric groups ⋮ Stanley character formula for the spin characters of the symmetric groups ⋮ Asymptotics for skew standard Young tableaux via bounds for characters ⋮ Quasi-symmetric functions as polynomial functions on Young diagrams

Cites Work

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• Stanley's formula for characters of the symmetric group.
• Matrix integrals and map enumeration: an accessible introduction
• Explicit combinatorial interpretation of Kerov character polynomials as numbers of permutation factorizations
• The combinatorial relationship between trees, cacti and certain connection coefficients for the symmetric group
• Representations of symmetric groups and free probability
• A refinement of Wigner's semicircle law in a neighborhood of the spectrum edge for random symmetric matrices
• Some properties of crossings and partitions
• Irreducible symmetric group characters of rectangular shape.
• Upper bound on the characters of the symmetric groups
• Upper bound on the characters of the symmetric groups for balanced Young diagrams and a generalized Frobenius formula.
• Free Random Variables
• Combinatorial theory of the free product with amalgamation and operator-valued free probability theory

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