On representations of real Jacobi groups
文献类型：期刊论文
| 作者 | Sun BinYong |
| 刊名 | SCIENCE CHINA-MATHEMATICS
 |
| 出版日期 | 2012 |
| 卷号 | 55期号:3页码:541-555 |
| 关键词 | LIE-GROUPS Jacobi group Heisenberg group irreducible representation matrix coefficient Gelfand-Kazhdan criterion |
| ISSN号 | 1674-7283 |
| 其他题名 | On representations of real Jacobi groups |
| 英文摘要 | We consider a category of continuous Hilbert space representations and a category of smooth Fr,chet representations, of a real Jacobi group G. By Mackey's theory, they are respectively equivalent to certain categories of representations of a real reductive group (L) over tilde. Within these categories, we show that the two functors that take smooth vectors for G and for (L) over tilde are consistent with each other. By using Casselman-Wallach's theory of smooth representations of real reductive groups, we define matrix coefficients for distributional vectors of certain representations of G. We also formulate Gelfand-Kazhdan criteria for real Jacobi groups which could be used to prove multiplicity one theorems for Fourier-Jacobi models. |
| 资助项目 | [National Natural Science Foundation of China] |
| 语种 | 英语 |
| CSCD记录号 | CSCD:4537854 |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/54346]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 作者单位 | 中国科学院数学与系统科学研究院 |
| 推荐引用方式 GB/T 7714 | Sun BinYong. On representations of real Jacobi groups[J]. SCIENCE CHINA-MATHEMATICS,2012,55(3):541-555. |
| APA | Sun BinYong.(2012).On representations of real Jacobi groups.SCIENCE CHINA-MATHEMATICS,55(3),541-555. |
| MLA | Sun BinYong."On representations of real Jacobi groups".SCIENCE CHINA-MATHEMATICS 55.3(2012):541-555. |
入库方式： OAI收割
来源：数学与系统科学研究院
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