A Cubic E-6-Generalization of the Classical Theorem on Harmonic Polynomials
文献类型：期刊论文
| 作者 | Xu, Xiaoping
|
| 刊名 | JOURNAL OF LIE THEORY
 |
| 出版日期 | 2011 |
| 卷号 | 21期号:1页码:145-164 |
| 关键词 | Harmonic polynomial E-6 Lie algebra irreducible module Dickson invariant invariant differential operator solution space |
| ISSN号 | 0949-5932 |
| 英文摘要 | Classical harmonic analysis says that the spaces of homogeneous harmonic polynomials (solutions of Laplace equation) are irreducible modules of the corresponding orthogonal Lie group (algebra) and the whole polynomial algebra is a free module over the invariant polynomials generated by harmonic polynomials. Dickson invariant trilinear form is the unique fundamental invariant in the polynomial algebra over the basic irreducible module of E-6. In this paper, we prove that the space of homogeneous polynomial solutions with degree in for the dual cubic Dickson invariant differential operator is exactly a direct sum of [m/2] + 1 explicitly determined irreducible E-6-submodules and the whole polynomial algebra is a free module over the polynomial algebra in the Dickson invariant generated by these solutions. Thus we obtain a cubic E-6-generalization of the above classical theorem on harmonic polynomials. |
| 语种 | 英语 |
| WOS记录号 | WOS:000288050000007 |
| 出版者 | HELDERMANN VERLAG |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/12108]  |
| 专题 | 数学所 |
| 通讯作者 | Xu, Xiaoping |
| 作者单位 | Chinese Acad Sci, Hua Loo Keng Key Math Lab, Inst Math, Acad Math & Syst Sci, Beijing 100190, Peoples R China |
| 推荐引用方式 GB/T 7714 | Xu, Xiaoping. A Cubic E-6-Generalization of the Classical Theorem on Harmonic Polynomials[J]. JOURNAL OF LIE THEORY,2011,21(1):145-164. |
| APA | Xu, Xiaoping.(2011).A Cubic E-6-Generalization of the Classical Theorem on Harmonic Polynomials.JOURNAL OF LIE THEORY,21(1),145-164. |
| MLA | Xu, Xiaoping."A Cubic E-6-Generalization of the Classical Theorem on Harmonic Polynomials".JOURNAL OF LIE THEORY 21.1(2011):145-164. |
入库方式： OAI收割
来源：数学与系统科学研究院
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