Representation Theory of Lie Groups

✍ Scribed by M. F. Atiyah, R. Bott, S. Helgason, D. Kazhdan, B. Kostant, G. Lustztig, eds.

• Publisher: Cambridge University Press
• Year: 1980
• Tongue: English
• Leaves: 341
• Series: London Mathematical Society Lecture Note Series 34
• Category: Library

✦ Synopsis

Lie groups and their representations occupy an important place in mathematics with applications in such diverse fields as differential geometry, number theory, differential equations and physics. In 1977 a symposium was held in Oxford to introduce this rapidly developing and expanding subject to non-specialists. This volume contains the lectures of ten distinguished mathematicians designed to provide the reader with a deeper understanding of the fundamental theory and appreciate the range of results. This volume contains much to interest mathematicians and theoretical physicists from advanced undergraduate level upwards.

✦ Table of Contents

Representation Theory of Lie Groups......Page 1
Contents......Page 3
1. Introduction......Page 5
2. Origins and early history of the theory of unitary group representations......Page 7
3. Induced representations......Page 22
4. The geometry and representation theory of compact Lie groups......Page 67
5. Algebraic structure of Lie groups......Page 93
6. Lie groups and physics......Page 153
7. The Harish-Chandra character......Page 178
8. Representations of semi-simple Lie groups......Page 185
9. Invariant differential operators and eigenspace representations......Page 236
10. Quantization and representation theory......Page 287
11. Integral geometry and representation theory......Page 317
12. On the reflection representation of a finite Chevalley group......Page 325
Index......Page 339