SL2(R)

1. Front Matter

   Pages i-xiv

   PDF

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

    PDF

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.

• Irreducibility
• Lie algebra
• algebra
• field
• lie group
• number theory
• representation theory

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

  Serge Lang

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