Combinatorial theory of Macdonald polynomials I: proof of Haglund's formula.
Haglund recently proposed a combinatorial interpretation of the modified Macdonald polynomials H(mu). We give a combinatorial proof of this conjecture, which establishes the existence and integrality of H(mu). As corollaries, we obtain the cocharge formula of Lascoux and Schutzenberger 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 J(mu), a formula for H(mu) in terms of Lascoux-Leclerc-Thibon polynomials, and combinatorial expressions for the Kostka-Macdonald coefficients K(lambda,mu) when mu is a two-column shape.
Haglund
J
J
Department of Mathematics, University of Pennsylvania, Philadelphia, PA 19104-6395, USA. jhaglund@math.upenn.edu
Haiman
M
M
Loehr
N
N