English

Jack polynomials and free cumulants

Combinatorics 2009-10-11 v3 Probability Representation Theory

Abstract

We study the coefficients in the expansion of Jack polynomials in terms of power sums. We express them as polynomials in the free cumulants of the transition measure of an anisotropic Young diagram. We conjecture that such polynomials have nonnegative integer coefficients. This extends recent results about normalized characters of the symmetric group.

Keywords

Cite

@article{arxiv.0802.0448,
  title  = {Jack polynomials and free cumulants},
  author = {Michel Lassalle},
  journal= {arXiv preprint arXiv:0802.0448},
  year   = {2009}
}

Comments

43 pages, LaTeX, to appear in Adv. Math

R2 v1 2026-06-21T10:09:23.153Z