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

Autor(es)

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

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: ADVANCES IN MATHEMATICS; v. 223, n. 3, p. 773-796, FEB 15 2010.
• Citações Web of Science: 16

Resumo

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)

• Processo FAPESP: 05/60337-2 - Álgebras de Lie e de Jordan, suas representações e generalizações
• Beneficiário: Ivan Chestakov
• Modalidade de apoio: Auxílio à Pesquisa - Temático