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.
 Publication:

arXiv eprints
 Pub Date:
 November 2009
 DOI:
 10.48550/arXiv.0911.1038
 arXiv:
 arXiv:0911.1038
 Bibcode:
 2009arXiv0911.1038D
 Keywords:

 Mathematics  Combinatorics;
 Mathematics  Representation Theory;
 20C30;
 05A15
 EPrint:
 Journal of Combinatorial Theory, Series A, 119 (6), 2012, pp 11741193