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

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

2008-06-20

arxiv.org/abs/0806.3292v1

Mathematics

Combinatorics

8 pages; contains streamlined and strengthened version of some of the results of arXiv:math/0612733

Scientific paper

We study the coinvariant ring of the complex reflection group $G(r,p,n)$ as a module for the corresponding rational Cherednik algebra $\HH$ 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 and Bagno and Biagoli. The irreducible $\mathcal{H}$-submodules of the coinvariant ring are their ``colored descent representations''.

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