Asymptotics of characters of symmetric groups: structure of Kerov character polynomials

Abstract

We study asymptotics of characters of the symmetric groups on a fixed conjugacy class. It was proved by Kerov that such a character can be expressed as a polynomial in free cumulants of the Young diagram (certain functionals describing the shape of the Young diagram). We show that for each genus there exists a universal symmetric polynomial which gives the coefficients of the part of Kerov character polynomials with the prescribed homogeneous degree. The existence of such symmetric polynomials was conjectured by Lassalle.

References in corpus (4)

• Explicit combinatorial interpretation of Kerov character polynomials as numbers of permutation factorizations
• Asymptotics of characters of symmetric groups, genus expansion and free probability
• Asymptotics of characters of symmetric groups related to Stanley character formula
• On the formula of Goulden and Rattan for Kerov polynomials

Cited by in corpus (1)

• Gaussian fluctuations of Young diagrams and structure constants of Jack characters