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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Jack polynomials and the coinvariant ring of $G(r,p,n)$
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by Stephen Griffeth PDF
Proc. Amer. Math. Soc. 137 (2009), 1621-1629 Request permission

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
  • © 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