On representations of real Jacobi groups

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	On representations of real Jacobi groups
其他题名	On representations of real Jacobi groups
	Sun BinYong
	2012
发表期刊	SCIENCE CHINA-MATHEMATICS
ISSN	1674-7283
卷号	55 期号:3 页码:541-555
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.
其他摘要	We consider a category of continuous Hilbert space representations and a category of smooth Fr’echet 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.Within these categories,we show that the two functors that take smooth vectors for G and for L 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.
关键词	LIE-GROUPS Jacobi group Heisenberg group irreducible representation matrix coefficient Gelfand-Kazhdan criterion
收录类别	CSCD
语种	英语
资助项目	[National Natural Science Foundation of China]
CSCD记录号	CSCD:4537854
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/54347
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.