Structure coefficients for Jack characters: approximate factorization property

Abstract

Jack characters are a generalization of the characters of the symmetric groups; a generalization that is related to Jack symmetric functions. We investigate the structure coefficients for Jack characters; they are a generalization of the connection coefficients for the symmetric groups. More specifically, we study the cumulants which measure the discrepancy between these structure coefficients and the simplistic structure coefficients related to the disjoint product. We show that Jack characters satisfy approximate factorization property: their cumulants are of very small degree and the character related to a given partition is approximately equal to the product of the characters related to its parts. This result will play a key role in the proof of Gaussianity of fluctuations for a class of random Young diagrams related to the Jack polynomials.

This paper has been withdrawn by the author because it was merged with arXiv:1506.06361

References in corpus (3)

• Jack polynomials and free cumulants
• A conjectured combinatorial interpretation of the normalized irreducible character values of the symmetric group
• The uses of random partitions

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• Random strict partitions and random shifted tableaux
• A Spin Analogue of Kerov Polynomials
• The top-degree part in the Matchings-Jack Conjecture
• Bijection between oriented maps and weighted non-oriented maps
• Algebras with two multiplications and their cumulants
• Jack characters and enumeration of maps