Representations of shifted Yangians and finite W-algebras

TL;DR

This paper classifies finite-dimensional irreducible representations of shifted Yangians and explains how to compute their characters using Kazhdan-Lusztig polynomials, linking shifted Yangians to finite W-algebras.

Contribution

It provides a classification of irreducible representations of shifted Yangians and a method to compute their characters via known polynomials, connecting to finite W-algebras.

Findings

Classification of finite-dimensional irreducible representations.

Method to compute Gelfand-Tsetlin characters.

Connection between shifted Yangians and W-algebras.

Abstract

We study highest weight representations of shifted Yangians over an algebraically closed field of characteristic 0. In particular, we classify the finite dimensional irreducible representations and explain how to compute their Gelfand-Tsetlin characters in terms of known characters of standard modules and certain Kazhdan-Lusztig polynomials. Our approach exploits the relationship between shifted Yangians and the finite W-algebras associated to nilpotent orbits in general linear Lie algebras.