Jack polynomials and free cumulants

By Michel Lassalle. 2008

55 citations recorded by the source corpus.

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.

Subfields: Discrete Mathematics and Combinatorics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/86f094137696f2d4e062883aa6f217b64e9712b7

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In Discrete Mathematics and Combinatorics

1. Valentin F'eray
2. Maciej Dolkega
3. Michel Lassalle

In Mathematical Physics

1. Maciej Dolkega
2. Valentin F'eray
3. Michel Lassalle

In Statistics and Probability

1. Valentin F'eray
2. Maciej Dolkega
3. Michel Lassalle

Citations in the corpus

• A positivity conjecture for Jack polynomials (2007, result): “Secondly in this article = 1 was of course never considered as being independent of . However in a subsequent paper [ 9 ], we have given an algorithm allowing to define the quantities # µ when (, ) are two independent parameters.”
• GAUSSIAN FLUCTUATIONS OF YOUNG DIAGRAMS AND STRUCTURE CONSTANTS OF JACK CHARACTERS (2014, methodology): “ as a polynomial in free cumulants. As it was first considered by Kerov in the case α = 1, it is usually termed Kerov’s polynomial (or Kerov’s expansion to avoid repetition of the word polynomial). In [Las09], Lassalle has described an inductive algorithm to compute the coeffi- cients of this expansio”