Quantizing Mishchenko-Fomenko subalgebras for centralizers via affine W-algebras

TL;DR

This paper introduces a method to quantize Mishchenko-Fomenko subalgebras associated with centralizers of nilpotent elements in simple Lie algebras using affine W-algebras, applicable in many cases including type A.

Contribution

It provides a novel quantization approach for Mishchenko-Fomenko subalgebras via affine W-algebras, extending previous methods to broader classes of Lie algebras.

Findings

Quantization achieved for all type A cases.

Quantization achieved for all minimal nilpotent cases outside type E8.

Method relies on affine W-algebras under certain assumptions.

Abstract

We use affine W-algebras to quantize Mishchenko-Fomenko subalgebras for centralizers of nilpotent elements in simple Lie algebras under certain assumptions that are satisfied for all cases in type A and all minimal nilpotent cases outside type $E_8$.