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Selecta Mathematica

, Volume 16, Issue 4, pp 791–818 | Cite as

Generalized Jack polynomials and the representation theory of rational Cherednik algebras

  • Charles Dunkl
  • Stephen Griffeth
Article

Abstract

We apply the Dunkl–Opdam operators and generalized Jack polynomials to study category \({{\mathcal O}_c}\) for the rational Cherednik algebra of type G(r, p, n). We determine the set of aspherical values and, in case p = 1, answer a question of Iain Gordon on the ordering of category \({{\mathcal O}_c}\) .

Keywords

Cherednik algebras Jack polynomials Norm formulae Morita equivalence 

Mathematics Subject Classification (2010)

Primary 05E05 05E10 05E15 16S35 20C30 Secondary 16D90 16S38 16T30 

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Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of VirginiaCharlottesvilleUSA
  2. 2.School of MathematicsUniversity of EdinburghEdinburghUK

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