A Graded Representation Model for Macdonald's Polynomials

We define doubly graded Snmodules Rμfor which we conjecture that the multiplicities of irreducible representations in various bi-degrees are given by the Macdonald coefficients Kλμ. Assuming one fundamental conjecture, the modules Rμcan be given several equivalent definitions, which we discuss. We p...

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Veröffentlicht in:	Proceedings of the National Academy of Sciences - PNAS 1993-04, Vol.90 (8), p.3607-3610
Hauptverfasser:	Garsia, Adriano M., Haiman, Mark
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebra Coefficients Commutative rings and algebras Coordinate systems Exact sciences and technology Mathematical functions Mathematical induction Mathematical rings Mathematical theorems Mathematics Polynomials Sciences and techniques of general use Symmetry
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Zusammenfassung:	We define doubly graded Snmodules Rμfor which we conjecture that the multiplicities of irreducible representations in various bi-degrees are given by the Macdonald coefficients Kλμ. Assuming one fundamental conjecture, the modules Rμcan be given several equivalent definitions, which we discuss. We prove the conjectures in various special cases.
ISSN:	0027-8424 1091-6490
DOI:	10.1073/pnas.90.8.3607