The Gelfand-kirillov Dimensions of Algebras Arising from Representation Theory
نویسنده
چکیده
This note is to study a variety of graded algebras that arise from the induced representations for semisimple algebraic groups and quantum groups. These algebras will play an important role in a study of the cohomology groups of line bundles over the flag varieties. This short note concentrates on the calculation of the Gelfand-Kirillov dimensions of these algebras.
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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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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We consider algebras over a field K presented by generators x1, . . . , xn and subject to (n 2 ) square-free relations of the form xixj = xkxl with every monomial xixj , i = j, appearing in one of the relations. It is shown that for n > 1 the Gelfand-Kirillov dimension of such an algebra is at least two if the algebra satisfies the so-called cyclic condition. It is known that this dimension is ...
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متن کاملLie Algebras with Finite Gelfand-kirillov Dimension
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تاریخ انتشار 2005