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

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- by Stephen Griffeth
- Proc. Amer. Math. Soc.
**137**(2009), 1621-1629 - DOI: https://doi.org/10.1090/S0002-9939-08-09697-4
- Published electronically: December 11, 2008
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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”.## References

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## Bibliographic 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
- © Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc.
**137**(2009), 1621-1629 - MSC (2000): Primary 05E10
- DOI: https://doi.org/10.1090/S0002-9939-08-09697-4
- MathSciNet review: 2470820