Elements of the representation theory of the Jacobi group /
The Jacobi group is a semidirect product of a symplectic group with a Heisenberg group. It is an important example for a non-reductive group and sets the frame within which to treat theta functions as well as elliptic functions - in particular, the universal elliptic curve. This text gathers for the...
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| Format: | eBook |
| Language: | English |
| Published: |
Basel ; Boston :
Birkhäuser Verlag,
[1998]
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| Series: | Progress in mathematics (Boston, Mass.) ;
vol. 163. |
| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
| Summary: | The Jacobi group is a semidirect product of a symplectic group with a Heisenberg group. It is an important example for a non-reductive group and sets the frame within which to treat theta functions as well as elliptic functions - in particular, the universal elliptic curve. This text gathers for the first time material from the representation theory of this group in both local (archimedean and non-archimedean) cases and in the global number field case. Via a bridge to Waldspurger's theory for the metaplectic group, complete classification theorems for irreducible representations are obtained. Further topics include differential operators, Whittaker models, Hecke operators, spherical representations and theta functions. The global theory is aimed at the correspondence between automorphic representations and Jacobi forms. This volume is thus a complement to the seminal book on Jacobi forms by M. Eichler and D. Zagier. Incorporating results of the authors' original research, this exposition is meant for researchers and graduate students interested in algebraic groups and number theory, in particular, modular and automorphic forms. |
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| Item Description: | Electronic resource. |
| Physical Description: | 1 online resource (xiii, 213 pages) |
| Format: | Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. |
| Bibliography: | Includes bibliographical references (pages 201-205) and indexes. |
| ISBN: | 9783034887724 (electronic bk.) 3034887728 (electronic bk.) |