Generalized Jack polynomials and the representation theory of rational Cherednik algebras

Abstract

We apply the Dunkl-Opdam operators and generalized Jack polynomials to study category O for the rational Cherednik algebra of type G(r,1,n). We determine the set of aspherical values, and answer a question of Iain Gordon on the ordering of category O.

20 pages; v2 updated based on reviewer feedback, now with somewhat expanded exposition and proofs

References in corpus (5)

• Blocks of cyclotomic Hecke algebras
• Orthogonal functions generalizing Jack polynomials
• Parabolic induction and restriction functors for rational Cherednik algebras
• Symmetric and Antisymmetric Vector-valued Jack Polynomials
• Finite dimensional representations of symplectic reflection algebras associated to wreath products II

Cited by in corpus (1)

• Blocks of restricted rational Cherednik algebras for $G(m,d,n)$