Twisted Yangians and finite W-algebras

TL;DR

This paper constructs explicit generators for certain finite W-algebras linked to symplectic and orthogonal Lie algebras and demonstrates they are quotients of twisted Yangians, advancing understanding of their algebraic structure.

Contribution

It provides explicit generators for finite W-algebras associated with specific nilpotent matrices and establishes their relationship as quotients of twisted Yangians.

Findings

Finite W-algebras are shown to be quotients of twisted Yangians.

Explicit generators for these W-algebras are constructed.

The work applies to nilpotent matrices with uniform Jordan block sizes.

Abstract

We construct an explicit set of generators for the finite W-algebras associated to nilpotent matrices in the symplectic or orthogonal Lie algebras whose Jordan blocks are all of the same size. We use these generators to show that such finite W-algebras are quotients of twisted Yangians.