MIT Combinatorics Seminar

A combinatorial model for the Macdonald polynomials

Jim Haglund  (UPenn)

Wednesday, December 08, 2004    4:15 pm    Room 2-338


We discuss a recent result of the speaker, M. Haiman and N. Loehr, which gives a combinatorial formula for the coefficient of a monomial in the Macdonald polynomial. The formula was first discovered by the speaker using experimental methods. Corollaries include a new proof of the +Lascoux-Schutzenberger cocharge formula for Hall-Littlewood polynomials, a combinatorial formula of Sahi and Knop for Jack symmetric functions, and a decomposition of Macdonald polynomials into the LLT polynomials of Lascoux, Leclerc and Thibon.