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Positive formula for Jack polynomials, Jack characters and proof of Lassalle's conjecture

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arxiv 2305.07966 v1 pith:U5TZ5WZU submitted 2023-05-13 math.CO

Positive formula for Jack polynomials, Jack characters and proof of Lassalle's conjecture

Houcine Ben Dali , Maciej Do{\l}\k{e}ga This is my paper
classification math.CO
keywords jackformulacharacterspolynomialsconjecturegivelassallebipartite
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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.

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Cited by 4 Pith papers

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    Introduces operator Γ yielding a creation formula for Macdonald polynomials, defines Macdonald characters, and poses positivity conjectures extending those on Jack polynomials.

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    A differential expression is established for the Jack analog of the super nabla operator via Chapuy-Dołęga and dehomogenized Nazarov-Sklyanin operators, derived from a general structure-coefficient operator G.

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