Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Jack polynomials and the coinvariant ring of

Author(s): Stephen Griffeth
Journal: Proc. Amer. Math. Soc. 137 (2009), 1621-1629.
MSC (2000): Primary 05E10
Posted: December 11, 2008
MathSciNet review: 2470820
Retrieve article in: PDF

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Abstract: We study the coinvariant ring of the complex reflection group as a module for the corresponding rational Cherednik algebra $\mathbb{H}$ and its generalized graded affine Hecke subalgebra $\mathcal{H}$ . We construct a basis consisting of non-symmetric Jack polynomials and, using this basis, decompose the coinvariant ring into irreducible modules for $\mathcal{H}$ . The basis consists of certain non-symmetric Jack polynomials whose leading terms are the ``descent monomials'' for recently studied by Adin, Brenti, and Roichman as well as Bagno and Biagoli. The irreducible $\mathcal{H}$ -submodules of the coinvariant ring are their ``colored descent representations''.

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