Combinatorial theory of Macdonald polynomials I: Proof of Haglund's formula
AUTOR(ES)
Haglund, J.
FONTE
National Academy of Sciences
RESUMO
Haglund recently proposed a combinatorial interpretation of the modified Macdonald polynomials H̃μ. We give a combinatorial proof of this conjecture, which establishes the existence and integrality of H̃μ. As corollaries, we obtain the cocharge formula of Lascoux and Schützenberger for Hall–Littlewood polynomials, a formula of Sahi and Knop for Jack's symmetric functions, a generalization of this result to the integral Macdonald polynomials Jμ, a formula for H̃μ in terms of Lascoux–Leclerc–Thibon polynomials, and combinatorial expressions for the Kostka–Macdonald coefficients K̃λ,μ when μ is a two-column shape.
