The Jacobi Group

1998 ◽  
pp. 1-14
Author(s):  
Rolf Berndt ◽  
Ralf Schmidt
Keyword(s):  
Jacobi Group

scholarly journals A Jacobi theta series and its transformation laws

2014 ◽  
Vol 10 (06) ◽  
pp. 1343-1354
Author(s):  
Matthew Krauel
Keyword(s):  
Vertex Operator ◽  
Operator Algebras ◽  
Theta Series ◽  
Jacobi Form ◽  
Vertex Operator Algebras ◽  
Jacobi Forms ◽  
Jacobi Group

We consider a generalization of Jacobi theta series and show that every such function is a quasi-Jacobi form. Under certain conditions we establish transformation laws for these functions with respect to the Jacobi group and prove such functions are Jacobi forms. In establishing these results, we construct other functions which are also Jacobi forms. These results are motivated by applications in the theory of vertex operator algebras.

scholarly journals Gaussian distributions, Jacobi group, and Siegel-Jacobi space

2014 ◽  
Vol 55 (12) ◽  
pp. 122102 ◽  
Author(s):  
Mathieu Molitor
Keyword(s):  
Gaussian Distributions ◽  
Jacobi Group

scholarly journals Generalized squeezed states for the Jacobi group

2008 ◽  
Author(s):  
S. Berceanu ◽  
Piotr Kielanowski ◽  
Anatol Odzijewicz ◽  
Martin Schlichenmaier ◽  
Theodore Voronov
Keyword(s):  
Squeezed States ◽  
Jacobi Group

scholarly journals ON THE GEOMETRY OF SIEGEL–JACOBI DOMAINS

2011 ◽  
Vol 08 (08) ◽  
pp. 1783-1798 ◽  
Author(s):  
S. BERCEANU ◽  
A. GHEORGHE
Keyword(s):  
Discrete Series ◽  
Unitary Representations ◽  
Fock Spaces ◽  
Holomorphic Discrete Series ◽  
Orthonormal Bases ◽  
Jacobi Group ◽  
Representation Spaces

We study the holomorphic unitary representations of the Jacobi group based on Siegel–Jacobi domains. Explicit polynomial orthonormal bases of the Fock spaces based on the Siegel–Jacobi disk are obtained. The scalar holomorphic discrete series of the Jacobi group for the Siegel–Jacobi disk is constructed and polynomial orthonormal bases of the representation spaces are given.

scholarly journals Vlasov moment flows and geodesics on the Jacobi group

2012 ◽  
Vol 53 (12) ◽  
pp. 123502 ◽  
Author(s):  
François Gay-Balmaz ◽  
Cesare Tronci
Keyword(s):  
Jacobi Group
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