Infinitesimal Cherednik algebras as W-algebras

TL;DR

This paper establishes an isomorphism between universal infinitesimal Cherednik algebras and W-algebras for certain Lie algebras, leading to new fundamental insights about the structure of infinitesimal Cherednik algebras.

Contribution

It introduces a novel isomorphism linking infinitesimal Cherednik algebras with W-algebras for specific Lie algebra types and nilpotent elements.

Findings

Proves an isomorphism between the two algebraic structures.

Derives fundamental properties of infinitesimal Cherednik algebras.

Provides a new perspective on the structure of these algebras.

Abstract

In this article we establish an isomorphism between universal infinitesimal Cherednik algebras and W-algebras for Lie algebras of the same type and 1-block nilpotent elements. As a consequence we obtain some fundamental results about infinitesimal Cherednik algebras.