Affinity of Cherednik algebras on projective space

TL;DR

This paper establishes conditions under which Cherednik algebra sheaves on projective space are affine, introducing a new concept of pull-back of modules to facilitate the analysis.

Contribution

It provides sufficient criteria for the affinity of Cherednik algebra sheaves on projective space and introduces the notion of pull-back of modules under flat morphisms.

Findings

Identified conditions ensuring affinity of Cherednik algebra sheaves

Developed a new framework for pull-back of modules

Enhanced understanding of Cherednik algebra structures on projective space

Abstract

We give sufficient conditions for the affinity of Etingof's sheaves of Cherednik algebras on projective space. To do this we introduce the notion of pull-back of modules under certain flat morphisms.