Restricted root systems and spin representations

doi:10.1007/s10468-007-9061-6

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	Restricted root systems and spin representations
	Han, Gang ; Sun, Bin-Yong
刊名	ALGEBRAS AND REPRESENTATION THEORY
	2007-10-01
卷号	10 期号:5 页码:463-469
关键词	restricted root system Weyl group spin representation isotropy representation
ISSN号	1386-923X
DOI	10.1007/s10468-007-9061-6
英文摘要	Let g(0) be a real semisimple Lie algebra. Let g0 = t(0)circle plus p(0) be the corresponding Cartan decomposition and h(0) = t(0) circle plus a(0) be a maximally compact Cartan subalgebra of g(0). Let g(0) = t(0) circle plus p(0) and h = t(0)circle plus a(0) be the corresponding complexifications. The set Delta( g, t) consists of all the linear forms on t which are the restriction to t of the roots in the root system Delta( g, h) of g with respect to h. The main result of the paper is to prove that Delta( g, t) is also a ( maybe non- reduced) root system and its Weyl group can be identified with a subgroup of the Weyl group of Delta( g, h). Let Spin nu: t -> End S be the composition of the isotropy representation nu: -> t so( p) with the spin representation Spin nu: -> t so( p). End S. Finally as an application, we give a nice description of the t- module structure on S in terms of the restricted root system Delta( g, t) and its Weyl group.
WOS研究方向	Mathematics
语种	英语
出版者	SPRINGER
WOS记录号	WOS:000248910300004
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/4417]
专题	数学所
通讯作者	Han, Gang
作者单位	1.Zhejiang Univ, Dept Math, Hangzhou 310027, Peoples R China 2.CAS, Acad Math & Syst Sci, Beijing 10080, Peoples R China
推荐引用方式 GB/T 7714	Han, Gang,Sun, Bin-Yong. Restricted root systems and spin representations[J]. ALGEBRAS AND REPRESENTATION THEORY,2007,10(5):463-469.
APA	Han, Gang,&Sun, Bin-Yong.(2007).Restricted root systems and spin representations.ALGEBRAS AND REPRESENTATION THEORY,10(5),463-469.
MLA	Han, Gang,et al."Restricted root systems and spin representations".ALGEBRAS AND REPRESENTATION THEORY 10.5(2007):463-469.