A graded representation model for Macdonald's polynomials.
We define doubly graded Sn modules Rmu for which we conjecture that the multiplicities of irreducible representations in various bi-degrees are given by the Macdonald coefficients Klambdamu. Assuming one fundamental conjecture, the modules Rmu can be given several equivalent definitions, which we discuss. We prove the conjectures in various special cases.
Garsia
A M
AM
Department of Mathematics, University of Calfornia, San Diego, La Jolla, CA 92093-0112, USA.
Haiman
M
M