• 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”.
  • Access State: Open Access