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  • © 1998

Elements of the Representation Theory of the Jacobi Group

Birkhäuser

Part of the book series: Progress in Mathematics (PM, volume 163)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xiii
  2. The Jacobi Group

    • Rolf Berndt, Ralf Schmidt
    Pages 1-14
  3. Basic Representation Theory of the Jacobi Group

    • Rolf Berndt, Ralf Schmidt
    Pages 15-30
  4. Local Representations: The Real Case

    • Rolf Berndt, Ralf Schmidt
    Pages 31-73
  5. The Space L 2J\G J(ℝ)) and its Decomposition

    • Rolf Berndt, Ralf Schmidt
    Pages 75-103
  6. Local Representations: The p-adic Case

    • Rolf Berndt, Ralf Schmidt
    Pages 105-136
  7. Spherical Representations

    • Rolf Berndt, Ralf Schmidt
    Pages 137-172
  8. Global Considerations

    • Rolf Berndt, Ralf Schmidt
    Pages 173-200
  9. Back Matter

    Pages 201-218

Reviews

"The book under review collects and regroups results on the representation theory of the Jacobi group of lowest degree mostly due to R.Berndt and his coworkers J.Homrighausen and R.Schmidt. The book is very well written and gives an up to date collection of the results known. It will be quite useful for everyone working in the field. The first chapter introduces the Jacobi group ~GJ, a semi-direct product of SL(2) with a Heisenberg group, and describes different possible coordinates on the group, the Haar measure, the Lie algebra, as well as, over the reals, a (generalized) Iwasawa decomposition and the associated homogeneous space..."

---Zentralblatt Math

"This book is an exposition which incorporates results of the authors' research works [that] will be very helpful for those who have some knowledge of the Jacquet-Langlands theory for GL2... Recommended for researchers interested in modular and automorphic forms."

---Mathematical Reviews

Authors and Affiliations

  • Mathematisches Seminar, Universität Hamburg, Hamburg, Germany

    Rolf Berndt, Ralf Schmidt

Bibliographic Information

  • Book Title: Elements of the Representation Theory of the Jacobi Group

  • Authors: Rolf Berndt, Ralf Schmidt

  • Series Title: Progress in Mathematics

  • DOI: https://doi.org/10.1007/978-3-0348-8772-4

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Basel AG 1998

  • Hardcover ISBN: 978-3-7643-5922-5Published: 19 May 1998

  • Softcover ISBN: 978-3-0348-9768-6Published: 23 August 2014

  • eBook ISBN: 978-3-0348-8772-4Published: 09 November 2013

  • Series ISSN: 0743-1643

  • Series E-ISSN: 2296-505X

  • Edition Number: 1

  • Number of Pages: XIII, 216

  • Number of Illustrations: 2 b/w illustrations

  • Topics: Number Theory, Group Theory and Generalizations

Buy it now

Buying options

eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access