A graded representation model for Macdonald's polynomials.

Proc Natl Acad Sci U S A

Department of Mathematics, University of Calfornia, San Diego, La Jolla, CA 92093-0112, USA.

Published: April 1993

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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http://www.ncbi.nlm.nih.gov/pmc/articles/PMC46350PMC
http://dx.doi.org/10.1073/pnas.90.8.3607DOI Listing

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Department of Mathematics, University of Calfornia, San Diego, La Jolla, CA 92093-0112, USA.

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