Totally aspherical parameters for Cherednik algebras

TL;DR

This paper introduces the concept of totally aspherical parameters in Rational Cherednik algebras, providing explicit constructions and proving their abundance for certain groups, which advances understanding of their representation theory.

Contribution

It defines totally aspherical parameters, constructs the associated projective objects explicitly, and proves their existence for groups G(l,1,n), enriching the theory of Cherednik algebras.

Findings

Explicit construction of the projective object for the KZ functor.

Existence of many totally aspherical parameters for G(l,1,n).

Enhanced understanding of the structure of Rational Cherednik algebras.

Abstract

We introduce the notion of a totally aspherical parameter for a Rational Cherednik algebra. We get an explicit construction of the projective object defining the KZ functor for such parameters. We establish the existence of sufficiently many totally aspherical parameters for the groups G(l,1,n).