Conformal oscillator representations of orthogonal Lie algebras

doi:10.1007/s11425-015-5058-5

CSpace > 数学所

	Conformal oscillator representations of orthogonal Lie algebras
	Xu XiaoPing1,2
	2016
发表期刊	SCIENCE CHINA-MATHEMATICS
ISSN	1674-7283
卷号	59 期号:1 页码:37-48
摘要	The conformal transformations with respect to the metric defining the orthogonal Lie algebra o(n, C) give rise to a one-parameter (c) family of inhomogeneous first-order differential operator representations of the orthogonal Lie algebra o(n+2, C). Letting these operators act on the space of exponential-polynomial functions that depend on a parametric vector , we prove that the space forms an irreducible o(n+2, C)-module for any c a C; if is not on a certain hypersurface. By partially swapping differential operators and multiplication operators, we obtain more general differential operator representations of o(n+2, C) on the polynomial algebra C in n variables. Moreover, we prove that C forms an infinite-dimensional irreducible weight o(n+2, C)-module with finite-dimensional weight subspaces if c is not an element of Z/2.
关键词	orthogonal Lie algebra differential operator oscillator representation irreducible module polynomial algebra exponential-polynomial function
DOI	10.1007/s11425-015-5058-5
语种	英语
资助项目	National Natural Science Foundation of China[11171324] ; National Natural Science Foundation of China[11321101]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000367346800003
出版者	SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/21656
专题	数学所
通讯作者	Xu XiaoPing
作者单位	1.Chinese Acad Sci, HUA Loo Keng Key Lab Math, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Xu XiaoPing. Conformal oscillator representations of orthogonal Lie algebras[J]. SCIENCE CHINA-MATHEMATICS,2016,59(1):37-48.
APA	Xu XiaoPing.(2016).Conformal oscillator representations of orthogonal Lie algebras.SCIENCE CHINA-MATHEMATICS,59(1),37-48.
MLA	Xu XiaoPing."Conformal oscillator representations of orthogonal Lie algebras".SCIENCE CHINA-MATHEMATICS 59.1(2016):37-48.