The authors study highest weight representations of shifted Yangians over an algebraically closed field of characteristic \(0\). In particular, they 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. The authors' approach exploits the relationship between shifted Yangians and the finite W-algebras associated to nilpotent orbits in general linear Lie algebras.

Table of Contents

• Introduction
• Shifted Yangians
• Finite W-algebras
• Dual canonical bases
• Highest weight theory
• Verma modules
• Standard modules
• Character formulae
• Notation
• Bibliography