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We study zonal characters which are defined as suitably normalized coefficients in the expansion of zonal polynomials in terms of power-sum symmetric functions.
The distribution of the latent roots of the covariance matrix
Alan T. James · 1960
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Zonal polynomials of the real positive definite symmetric matrices
Alan T. James · 1961
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Harmonic analysis of functions of several complex variables in the classical domains
L. K. Hua · 1963
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A class of symmetric polynomials with a parameter
Henry Jack · 1971
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Aspects of multivariate statistical theory
Robb J. Muirhead · 1982
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Zonal polynomials
Akimichi Takemura · 1984
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Jack symmetric functions and some combinatorial properties of Young symmetrizers
Phil Hanlon · 1988
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Some combinatorial properties of Jack symmetric functions
Richard P. Stanley · 1989
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Representation theory, a first course
W. Fulton and J. Harris · 1991
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Symmetric functions and Hall polynomials
I. G. Macdonald · 1995
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Maps in locally orientable surfaces, the double coset algebra, and zonal polynomials
I. P. Goulden and D. M. Jackson · 1996
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The Selberg-Jack symmetric functions
Kevin W. J. Kadell · 1997
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Shifted Jack polynomials, binomial formula, and applications
A. Okounkov and G. Olshanski · 1997
Cited alongside, same era.
Representations of symmetric groups and free probability
Philippe Biane · 1998
Cited alongside, same era.
The algebra of conjugacy classes in symmetric groups, and partial permutations
V. Ivanov and S. Kerov · 1999
Cited alongside, same era.
Talk in institute henri poincaré, paris
S. Kerov · 2000
Cited alongside, same era.
Gaussian fluctuations of characters of symmetric groups and of Young diagrams
Piotr Śniady · 2006
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A conjectured combinatorial interpretation of the normalized irreducible character values of the symmetric group
Richard P. Stanley · 2006
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Asymptotics of characters of symmetric groups related to Stanley character formula
Valentin Féray and Piotr Śniady · 2007
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A positivity conjecture for Jack polynomials
Michel Lassalle · 2008
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Upper bound on the characters of the symmetric groups for balanced Young diagrams and a generalized Frobenius formula
Amarpreet Rattan and Piotr Śniady · 2008
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Combinatorial interpretation and positivity of Kerov’s character polynomials
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A differential ideal of symmetric polynomials spanned by Jack polynomials at β = − ( r − 1 ) / ( k + 1 ) \beta=-(r-1)/(k+1)
B. Feigin, M. Jimbo, T. Miwa, and E. Mukhin · 2002
Cited alongside, same era.
Kerov’s central limit theorem for the Plancherel measure on Young diagrams
Vladimir Ivanov and Grigori Olshanski · 2002
Cited alongside, same era.
Characters of symmetric groups and free cumulants
Philippe Biane · 2003
Cited alongside, same era.
Irreducible symmetric group characters of rectangular shape
Richard P. Stanley · 2003
Cited alongside, same era.
Über die Charaktere der symmetrischen Gruppe
G. Frobenius
Cited in the paper.
Valentin Féray · 2009
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Jack polynomials and free cumulants
Michel Lassalle · 2009
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Representation Theory of the Symmetric Groups: The Okounkov-Vershik Approach, Character Formulas, and Partition Algebras
T. Ceccherini-Silberstein, F. Scarabotti, and F. Tolli · 2010
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Explicit combinatorial interpretation of Kerov character polynomials as numbers of permutation factorizations
Maciej Dołęga, Valentin Féray, and Piotr Śniady · 2010
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Stanley’s formula for characters of the symmetric group
V. Féray · 2010
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