The Gelfand-Kirillov conjecture and Gelfand-Tsetlin modules for finite W-algebras

By Vyacheslav Futorny, Alexander I. Molev, S. Ovsienko. 2010

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Abstract We address two problems with the structure and representation theory of finite W -algebras associated with general linear Lie algebras. Finite W -algebras can be defined using either Kostant's Whittaker modules or a quantum Hamiltonian reduction. Our first main result is a proof of the Gelfand–Kirillov conjecture for the skew fields of fractions of finite W -algebras. The second main result is a parameterization of finite families of irreducible Gelfand–Tsetlin modules using Gelfand–Tsetlin subalgebra. As a corollary, we obtain a complete classification of generic irreducible Gelfand–Tsetlin modules for finite W -algebras.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/0fec282579222584ad21693569e7d12470bd934e