Representations of Shifted Yangians and Finite $w$-algebras

Studies highest weight representations of shifted Yangians over an algebraically closed field of characteristic $0$. This book classifies the finite dimensional irreducible representations and explains how to compute their Gelfand-Tsetlin characters in terms of known characters of standard modules and certain Kazhdan-Lusztig polynomials.

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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.