Generalized Jack polynomials and the representation theory of rational Cherednik algebras

By Charles F. Dunkl, Stephen Griffeth. 2010

59 citations recorded by the source corpus.

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 $${{\mathcal O}_c}$$ .

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/ee186b9138e4e62e1d17a853f4703c5409beb744

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. I. Gordon
2. I. Losev
3. T. Nevins
4. Kevin McGerty
5. V. Ginzburg
6. Ben Webster
7. E. Gorsky
8. T. Arakawa

In Discrete Mathematics and Combinatorics

1. I. Losev
2. I. Gordon
3. Stephen Griffeth
4. Pavel Etingof
5. François Bergeron
6. Victor Reiner
7. Anne V. Shepler
8. S. Witherspoon

In Geometry and Topology

1. I. Gordon
2. I. Losev
3. T. Nevins
4. Kevin McGerty
5. V. Ginzburg
6. Pavel Etingof
7. Stephen Griffeth
8. E. Gorsky

Citations in the corpus

• Categorifications and cyclotomic rational double affine Hecke algebras (2013, unknown): “A previous work of Dunkl and Griffeth [20] allows to show without much difficulty that there is a highest weight order on O which refines the linkage order on A.”
• On category O for cyclotomic rational Cherednik algebras (2011, background): “Cherednik algebra, category O, derived category, deformation quantization, categorification”
• Derived equivalence for quantum symplectic resolutions (2011, background): “4, combining the constructions of [23,31] and the result of [19] on the aspherical values of the parameters gives the following result:”