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Proceedings of the National Academy of Sciences of the United States of America logoLink to Proceedings of the National Academy of Sciences of the United States of America
. 1993 Apr 15;90(8):3607–3610. doi: 10.1073/pnas.90.8.3607

A graded representation model for Macdonald's polynomials.

A M Garsia 1, M Haiman 1
PMCID: PMC46350  PMID: 11607377

Abstract

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.

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