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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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
DOI: https://doi.org/10.1090/S0002-9939-08-09697-4
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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Additional Information

Stephen Griffeth
Affiliation: Department of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
Email: griffeth@math.umn.edu

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.