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On representations of real Jacobi groups

Content Provider	Springer Nature Link
Author	Sun, BinYong
Copyright Year	2011
Abstract	We consider a category of continuous Hilbert space representations and a category of smooth Fréchet 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 $\tilde L$ . Within these categories, we show that the two functors that take smooth vectors for G and for $\tilde L$ 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.
Starting Page	541
Ending Page	555
Page Count	15
File Format	PDF
ISSN	16747283
Journal	Science in China Series A: Mathematics
Volume Number	55
Issue Number	3
e-ISSN	18691862
Language	English
Publisher	SP Science China Press
Publisher Date	2011-12-24
Publisher Place	Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Jacobi group Heisenberg group irreducible representation matrix coefficient Gelfand-Kazhdan criterion Applications of Mathematics
Content Type	Text
Resource Type	Article
Subject	Mathematics

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