The Gelfand-Kirillov conjecture and Gelfand-Tsetlin modules for finite W-algebras
| Contribuinte(s) |
UNIVERSIDADE DE SÃO PAULO |
|---|---|
| Data(s) |
20/10/2012
20/10/2012
2010
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| 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. Australian Research Council Australian Research Council CNPq[301743/2007-0] Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Fapesp[2005/60337-2] Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) University of Sydney University of Sydney |
| Identificador |
ADVANCES IN MATHEMATICS, v.223, n.3, p.773-796, 2010 0001-8708 http://producao.usp.br/handle/BDPI/30734 10.1016/j.aim.2009.08.018 |
| Idioma(s) |
eng |
| Publicador |
ACADEMIC PRESS INC ELSEVIER SCIENCE |
| Relação |
Advances in Mathematics |
| Direitos |
restrictedAccess Copyright ACADEMIC PRESS INC ELSEVIER SCIENCE |
| Palavras-Chave | #Gelfand-Tsetlin modules #Finite W-algebras #Shifted Yangian #Gelfand-Tsetlin conjecture #SOLVABLE LIE-ALGEBRAS #REPRESENTATION-THEORY #QUANTIZATION #REDUCTION #SLICES #Mathematics |
| Tipo |
article original article publishedVersion |
