Positive formula for Jack polynomials, Jack characters and proof of Lassalle's conjecture
Combinatorics
2023-05-16 v1
Abstract
We give an explicit formula for the power-sum expansion of Jack polynomials. We deduce it from a more general formula, which we provide here, that interprets Jack characters in terms of bipartite maps. We prove Lassalle's conjecture from 2008 on integrality and positivity of Jack characters in Stanley's coordinates and give a new formula for Jack polynomials using creation operators.
Keywords
Cite
@article{arxiv.2305.07966,
title = {Positive formula for Jack polynomials, Jack characters and proof of Lassalle's conjecture},
author = {Houcine Ben Dali and Maciej Dołęga},
journal= {arXiv preprint arXiv:2305.07966},
year = {2023}
}
Comments
44 pages, 3 figures