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Jack polynomials and the coinvariant ring of $ G(r,p,n)$

Author: Stephen Griffeth
Journal: Proc. Amer. Math. Soc. 137 (2009), 1621-1629
MSC (2000): Primary 05E10
Published electronically: December 11, 2008
MathSciNet review: 2470820
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Abstract: We study the coinvariant ring of the complex reflection group $ G(r,p,n)$ 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 $ G(r,p,n)$ 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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Stephen Griffeth
Affiliation: Department of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455

Received by editor(s): May 30, 2008
Received by editor(s) in revised form: July 13, 2008
Published electronically: December 11, 2008
Communicated by: Jim Haglund
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.