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SL2(R)

  • Textbook
  • © 1985

Overview

Authors:
  1. Serge Lang

    1. Department of Mathematics, Yale University, New Haven, USA

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Part of the book series: Graduate Texts in Mathematics (GTM, volume 105)

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About this book

SL2(R) gives the student an introduction to the infinite dimensional representation theory of semisimple Lie groups by concentrating on one example - SL2(R). This field is of interest not only for its own sake, but for its connections with other areas such as number theory, as brought out, for example, in the work of Langlands. The rapid development of representation theory over the past 40 years has made it increasingly difficult for a student to enter the field. This book makes the theory accessible to a wide audience, its only prerequisites being a knowledge of real analysis, and some differential equations.

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Table of contents (14 chapters)

  1. Front Matter

    Pages i-xiv
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  2. General Results

    • Serge Lang
    Pages 1-17

  3. Compact Groups

    • Serge Lang
    Pages 19-35

  4. Induced Representations

    • Serge Lang
    Pages 37-49

  5. Spherical Functions

    • Serge Lang
    Pages 51-65

  6. The Spherical Transform

    • Serge Lang
    Pages 67-88

  7. The Derived Representation on the Lie Algebra

    • Serge Lang
    Pages 89-126

  8. Traces

    • Serge Lang
    Pages 127-161

  9. The Plancherel Formula

    • Serge Lang
    Pages 163-177

  10. Discrete Series

    • Serge Lang
    Pages 179-190

  11. Partial Differential Operators

    • Serge Lang
    Pages 191-203

  12. The Weil Representation

    • Serge Lang
    Pages 205-217

  13. Representation on 0L2(Г\G)

    • Serge Lang
    Pages 219-238

  14. The Continuous Part of L2(Г\G)

    • Serge Lang
    Pages 239-262

  15. Spectral Decompositon of the Laplace Operator on Γ\\(\mathfrak{H}\)

    • Serge Lang
    Pages 263-352

  16. Back Matter

    Pages 353-431
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Authors and Affiliations

  • Department of Mathematics, Yale University, New Haven, USA

    Serge Lang

Bibliographic Information

  • Book Title: SL2(R)

  • Authors: Serge Lang

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-5142-2

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York Inc. 1985

  • Softcover ISBN: 978-1-4612-9581-5Published: 01 October 2011

  • eBook ISBN: 978-1-4612-5142-2Published: 06 December 2012

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 1

  • Number of Pages: XIV, 431

  • Additional Information: Originally published by Addison-Wesley Publishing Company, 1975

  • Topics: Algebra

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