Restricted root systems and spin representations
文献类型：期刊论文
| 作者 | Han, Gang; Sun, Bin-Yong
|
| 刊名 | ALGEBRAS AND REPRESENTATION THEORY
 |
| 出版日期 | 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 |
| WOS记录号 | WOS:000248910300004 |
| 出版者 | SPRINGER |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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