Jack polynomials and free cumulants

Details Jack polynomials and free cumulants Jack polynomials and free cumulants

2008-02-04

arxiv.org/abs/0802.0448v3

Advances in Mathematics 222 (2009) 2227-2269

Mathematics

Combinatorics

43 pages, LaTeX, to appear in Adv. Math

Scientific paper

10.1016/j.aim.2009.07.007

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.

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