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Media type:
E-Article
Title:
Jack polynomials and the coinvariant ring of 𝐺(𝑟,𝑝,𝑛)
Contributor:
Griffeth, Stephen
Published:
American Mathematical Society (AMS), 2008
Published in:
Proceedings of the American Mathematical Society, 137 (2008) 5, Seite 1621-1629
Language:
English
DOI:
10.1090/s0002-9939-08-09697-4
ISSN:
0002-9939;
1088-6826
Origination:
Footnote:
Description:
We study the coinvariant ring of the complex reflection group G ( r , p , n ) G(r,p,n) as a module for the corresponding rational Cherednik algebra H \mathbb {H} and its generalized graded affine Hecke subalgebra H \mathcal {H} . We construct a basis consisting of non-symmetric Jack polynomials and, using this basis, decompose the coinvariant ring into irreducible modules for H \mathcal {H} . The basis consists of certain non-symmetric Jack polynomials whose leading terms are the “descent monomials” for G ( r , p , n ) G(r,p,n) recently studied by Adin, Brenti, and Roichman as well as Bagno and Biagoli. The irreducible H \mathcal {H} -submodules of the coinvariant ring are their “colored descent representations”.