Jack polynomials and the coinvariant ring of $G(r,p,n)$
| dc.creator | Griffeth, Stephen | |
| dc.date | 2008-06-20 | |
| dc.date.accessioned | 2026-07-07T09:45:49Z | |
| dc.date.available | 2026-07-07T09:45:49Z | |
| dc.description | 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''. | |
| dc.description | 8 pages; contains streamlined and strengthened version of some of the results of arXiv:math/0612733 | |
| dc.identifier | https://arxiv.org/abs/0806.3292 | |
| dc.identifier | http://arxiv.org/abs/0806.3292 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/163325 | |
| dc.subject | Combinatorics | |
| dc.subject | Representation Theory | |
| dc.title | Jack polynomials and the coinvariant ring of $G(r,p,n)$ | |
| dc.type | text |