Flag partial differential equations and representations of lie algebras
文献类型：期刊论文
| 作者 | Xu, Xiaoping
|
| 刊名 | ACTA APPLICANDAE MATHEMATICAE
 |
| 出版日期 | 2008-07-01 |
| 卷号 | 102期号:2-3页码:249-280 |
| 关键词 | flag partial differential equation polynomial solution laplace equation wave equation tree diagram generalized Tricomi operator Lie algebra representation |
| ISSN号 | 0167-8019 |
| DOI | 10.1007/s10440-008-9217-3 |
| 英文摘要 | Flag partial differential equations naturally appear in the problem of decomposing the polynomial algebra (symmetric tensor) over an irreducible module of a Lie algebra into the direct sum of its irreducible submodules. Many important linear partial differential equations in physics and geometry are also of flag type. In this paper, we use the grading technique in algebra to develop the methods of solving such equations. In particular, we find new special functions by which we are able to explicitly give the solutions of the initial value problems of a large family of constant-coefficient linear partial differential equations in terms of their coefficients. As applications to representations of Lie algebras, we find certain explicit irreducible polynomial representations of the Lie algebras sl(n, F), so(n, F) and the simple Lie algebra of type G(2). |
| 语种 | 英语 |
| WOS记录号 | WOS:000256088400009 |
| 出版者 | SPRINGER |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/6388]  |
| 专题 | 数学所 |
| 通讯作者 | Xu, Xiaoping |
| 作者单位 | Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100080, Peoples R China |
| 推荐引用方式 GB/T 7714 | Xu, Xiaoping. Flag partial differential equations and representations of lie algebras[J]. ACTA APPLICANDAE MATHEMATICAE,2008,102(2-3):249-280. |
| APA | Xu, Xiaoping.(2008).Flag partial differential equations and representations of lie algebras.ACTA APPLICANDAE MATHEMATICAE,102(2-3),249-280. |
| MLA | Xu, Xiaoping."Flag partial differential equations and representations of lie algebras".ACTA APPLICANDAE MATHEMATICAE 102.2-3(2008):249-280. |
入库方式： OAI收割
来源：数学与系统科学研究院
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