Projective Oscillator Representations of sl(n+1) and sp (2m+2)

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	Projective Oscillator Representations of sl(n+1) and sp (2m+2)
	Xu, Xiaoping
刊名	JOURNAL OF LIE THEORY
	2016
卷号	26 期号:1 页码:97-115
关键词	Special linear Lie algebra symplectic Lie algebra oscillator representation irreducible module polynomial algebra exponential-polynomial function
ISSN号	0949-5932
英文摘要	The n-dimensional projective group gives rise to a one-parameter family of inhomogeneous first-order differential operator representations of sl (n + 1). By partially swapping differential operators and multiplication operators, we obtain more general differential operator representations of sl (n + 1). Letting these differential operators act on the corresponding polynomial algebra and the space of exponential-polynomial functions, we construct new multi-parameter families of explicit infinite-dimensional irreducible representations for sl (n + 1) and sp (2m + 2) when n = 2m + 1. Our results can be viewed as extensions of Howe's oscillator construction of infinite-dimensional multiplicity-free irreducible representations for sl (n). They can also be used to study free bosonic field irreducible representations of the corresponding affine Kac-Moody algebras.
语种	英语
出版者	HELDERMANN VERLAG
WOS记录号	WOS:000377235700005
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/22874]
专题	数学所
通讯作者	Xu, Xiaoping
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, Hua Loo Keng Key Math Lab, Inst Math, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Xu, Xiaoping. Projective Oscillator Representations of sl(n+1) and sp (2m+2)[J]. JOURNAL OF LIE THEORY,2016,26(1):97-115.
APA	Xu, Xiaoping.(2016).Projective Oscillator Representations of sl(n+1) and sp (2m+2).JOURNAL OF LIE THEORY,26(1),97-115.
MLA	Xu, Xiaoping."Projective Oscillator Representations of sl(n+1) and sp (2m+2)".JOURNAL OF LIE THEORY 26.1(2016):97-115.