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
	2011-02-15
发表期刊	JOURNAL OF ALGEBRA
ISSN	0021-8693
卷号	328 期号:1 页码:132-154
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.
关键词	Special linear Lie algebra Representation of Lie algebra Characteristic identities
DOI	10.1016/j.jalgebra.2010.07.009
语种	英语
资助项目	NSFC[10701002]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000286447400008
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/13108
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.