Totally Aspherical Parameters for Cherednik Algebras

The chapter delves into the concept of totally aspherical parameters for Cherednik algebras, focusing on their definition and implications. It explores the triangular decomposition of the rational Cherednik algebra H c ( W ) and the properties of its spherical subalgebra eH c ( W ) e. The text introduces the notion of totally aspherical parameters and their equivalence to the simplicity of the algebra eH c ( W ) e. It also investigates the relationship between the Harish-Chandra module and the projective object P KZ, highlighting the criteria for their equivalence. Additionally, the chapter applies these concepts to specific cases, such as the symmetric group and the groups G ( ℓ, 1, n ), providing insights into the existence and properties of totally aspherical parameters in these contexts.