ar X iv : 0 80 1 . 09 03 v 3 [ m at h . R A ] 6 J un 2 00 9 GELFAND - KIRILLOV CONJECTURE AND GELFAND - TSETLIN MODULES FOR FINITE W - ALGEBRAS
نویسنده
چکیده
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 modules 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 Gelfand-Tsetlin modules by the characters of the Gelfand-Tsetlin subalgebra. As a corollary, we obtain a complete classification of generic irreducible Gelfand-Tsetlin modules for the finite W -algebras. Mathematics Subject Classification 17B35, 17B37, 17B67, 16D60, 16D90, 16D70, 81R10
منابع مشابه
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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 modules 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 a...
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تاریخ انتشار 2009