Gelfand-Kirillov Conjecture and Harish-Chandra Modules for Finite W-Algebras
Rings and Algebras
2009-06-06 v3 Representation Theory
Abstract
We address two problems regarding the structure and representation theory of finite W-algebras associated with the general linear Lie algebras. Finite W-algebras can be defined either via the Whittaker model of Kostant or, equivalently, by the quantum Hamiltonian reduction. Our first main result is a proof of the Gelfand-Kirillov conjecture for the skew fields of fractions of the finite W-algebras. The second main result is a parametrization of finite families of irreducible Harish-Chandra modules by the characters of the Gelfand-Tsetlin subalgebra. As a corollary, we obtain a complete classification of generic irreducible Harish-Chandra modules for the finite W-algebras.
Keywords
Cite
@article{arxiv.0801.0903,
title = {Gelfand-Kirillov Conjecture and Harish-Chandra Modules for Finite W-Algebras},
author = {Vyacheslav Futorny and Alexander Molev and Serge Ovsienko},
journal= {arXiv preprint arXiv:0801.0903},
year = {2009}
}