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	Extensions of the conformal representations for orthogonal Lie algebras
	Xu, Xiaoping ; Zhao, Yufeng
	2013
关键词	Conformal transformation Polynomial algebra Tensor Pieri&apos Generalizations of the conformal representation Orthogonal Lie algebra Irreducibility CARTAN TYPE GRADED MODULES IRREDUCIBLE REPRESENTATIONS MULTIPLICITIES CLASSIFICATION FINITE TORUS s formula
英文摘要	The conformal transformations with respect to the metric defining o(n, C) give rise to an inhomogeneous polynomial representation of o(n + 2, C). Using Shen's technique of mixed product, we generalize the above representation to an inhomogeneous representation of o(n + 2, C) on the tensor space of any finite-dimensional irreducible o(n, C)-module with the polynomial space, where a hidden central transformation is involved. Moreover, we find a condition on the constant value taken by the central transformation such that the generalized representation is irreducible. In our approach, Pieri's formulas, invariant operators and the idea of Kostant's characteristic identities play key roles. The result could be useful in understanding higher-dimensional conformal field theory with the constant value taken by the central transformation as the central charge. Our representations virtually provide natural extensions of the conformal transformations on a Riemannian manifold to its vector bundles. (c) 2012 Elsevier Inc. All rights reserved.; Mathematics; SCI(E); 1; ARTICLE; 97-124; 377
语种	英语
出处	SCI
出版者	journal of algebra
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/225557]
专题	数学科学学院
推荐引用方式 GB/T 7714	Xu, Xiaoping,Zhao, Yufeng. Extensions of the conformal representations for orthogonal Lie algebras. 2013-01-01.

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