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

Author(s)

Futorny, Vyacheslav ^[1] ; Molev, Alexander ^[2] ; Ovsienko, Serge ^[3]

Affiliation

^[1] Univ Sao Paulo, Inst Math & Stat, BR-05315970 Sao Paulo - Brazil

^[2] Univ Sydney, Sch Math & Stat, Sydney, NSW 2006 - Australia

^[3] Kiev Taras Shevchenko Univ, Fac Mech & Math, UA-00133 Kiev - Ukraine

• Document type: Journal article
• Source: ADVANCES IN MATHEMATICS; v. 223, n. 3, p. 773-796, FEB 15 2010.
• Web of Science Citations: 16

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. (C) 2009 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 05/60337-2 - Lie and Jordan algebras, their representations and generalizations
• Grantee: Ivan Chestakov
• Support Opportunities: Research Projects - Thematic Grants