Conformal oscillator representations of orthogonal Lie algebras
文献类型：期刊论文
| 作者 | Xu XiaoPing1,2
|
| 刊名 | SCIENCE CHINA-MATHEMATICS
 |
| 出版日期 | 2016 |
| 卷号 | 59期号:1页码:37-48 |
| 关键词 | orthogonal Lie algebra differential operator oscillator representation irreducible module polynomial algebra exponential-polynomial function |
| ISSN号 | 1674-7283 |
| DOI | 10.1007/s11425-015-5058-5 |
| 英文摘要 | 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. |
| 语种 | 英语 |
| WOS记录号 | WOS:000367346800003 |
| 出版者 | SCIENCE PRESS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/21655]  |
| 专题 | 数学所 |
| 通讯作者 | Xu XiaoPing |
| 作者单位 | 1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100190, Peoples R China 2.Chinese Acad Sci, HUA Loo Keng Key Lab 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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