The Gelfand–Kirillov conjecture and Gelfand–Tsetlin modules for finite W-algebras
نویسندگان
چکیده
منابع مشابه
Gelfand - Kirillov Conjecture and Harish - Chandra Modules for Finite W - Algebras
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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A finite W -algebra U(g, e) is a certain finitely generated algebra that can be viewed as the enveloping algebra of the Slodowy slice to the adjoint orbit of a nilpotent element e of a complex reductive Lie algebra g. It is possible to give the tensor product of a U(g, e)-module with a finite dimensional U(g)module the structure of a U(g, e)-module; we refer to such tensor products as translati...
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The property of some finite W algebras to be the commutant of a particular subalgebra of a simple Lie algebra G is used to construct realizations of G. When G ≃ so(4, 2), unitary representations of the conformal and Poincaré algebras are recognized in this approach, which can be compared to the usual induced representation technique. When G ≃ sp(2,R) or sp(4,R ), the anyonic parameter can be se...
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New realizations of finite W-algebras are constructed by relaxing the usual constraint conditions. Then finite W-algebras are recognized in the Heisenberg quantization recently proposed by Leinaas and Myrheim, for a system of two identical particles in d dimensions. As the anyonic parameter is directly associated to the W-algebra involved in the d = 1 case, it is natural to consider that the W-...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2010
ISSN: 0001-8708
DOI: 10.1016/j.aim.2009.08.018