The inverse Galois problem for Cherednik algebras

TL;DR

This paper investigates the inverse Galois problem for Cherednik algebras, aiming to classify finite groups acting on certain domains such that the spherical subalgebra is their ring of invariants, using geometric methods.

Contribution

It provides a classification of finite groups related to Cherednik algebras via geometric analysis of the algebra's center in characteristic p.

Findings

Classification of groups acting on domains with Cherednik algebra invariants

Connection between group actions and geometry of the algebra's center

Results applicable to understanding symmetries in Cherednik algebras

Abstract

Given the spherical subalgebra $B$ of a rational Cherednik algebra, we aim to classify all finite groups $\Gamma$ for which there exists a domain $R$ on which $\Gamma$ acts by ring automorphisms, such that $B=R^{\Gamma}.$ We describe such groups in terms of geometry of the center of the reduction of $B$ modulo a large prime.