On representations of real Jacobi groups  

作　　者：SUN BinYong 

机构地区：[1]Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

出　　处：《Science China Mathematics》2012年第3期541-555,共15页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos. 10801126 and 10931006)

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.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：Jacobi group Heisenberg group irreducible representation matrix coefficient Gelfand-Kazhdancriterion 

分 类 号：O177.1[理学—数学] TB115[理学—基础数学]