Generalized projective representations for sl(n+1)

doi:10.1016/j.jalgebra.2010.07.009

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	Generalized projective representations for sl(n+1)
	Zhao, Yufeng 1; Xu, Xiaoping2
刊名	JOURNAL OF ALGEBRA
	2011-02-15
卷号	328 期号:1 页码:132-154
关键词	Special linear Lie algebra Representation of Lie algebra Characteristic identities
ISSN号	0021-8693
DOI	10.1016/j.jalgebra.2010.07.009
英文摘要	It is well known that n-dimensional projective group gives rise to a non-homogeneous representation of the Lie algebra sl(n + 1) on the polynomial functions of the projective space. Using Shen's mixed product for Witt algebras (also known as Larsson functor), we generalize the above representation of sl(n + 1) to a non-homogeneous representation on the tensor space of any finite-dimensional irreducible gl(n)-module with the polynomial space. Moreover, the structure of such a representation is completely determined by employing projection operator techniques and well-known Kostant's characteristic identities for certain matrices with entries in the universal enveloping algebra. In particular, we obtain a new one parameter family of infinite-dimensional irreducible sl(n + 1)-modules. which are in general not highest-weight type, for any given finite-dimensional irreducible sl(n)-module. The results could also be used to study the quantum field theory with the projective group as the symmetry. (C) 2010 Elsevier Inc. All rights reserved.
资助项目	NSFC[10701002]
WOS研究方向	Mathematics
语种	英语
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
WOS记录号	WOS:000286447400008
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/13107]
专题	数学所
通讯作者	Zhao, Yufeng
作者单位	1.Peking Univ, Sch Math Sci, LMAM, Beijing 100871, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Hua Loo Keng Key Math Lab, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Zhao, Yufeng,Xu, Xiaoping. Generalized projective representations for sl(n+1)[J]. JOURNAL OF ALGEBRA,2011,328(1):132-154.
APA	Zhao, Yufeng,&Xu, Xiaoping.(2011).Generalized projective representations for sl(n+1).JOURNAL OF ALGEBRA,328(1),132-154.
MLA	Zhao, Yufeng,et al."Generalized projective representations for sl(n+1)".JOURNAL OF ALGEBRA 328.1(2011):132-154.