Because of their significance in physics and chemistry, representation of Lie groups has been an area of intensive study by physicists and chemists, as well as mathematicians. This introduction is designed for graduate students who have some knowledge of finite groups and general topology, but is otherwise self-contained. The author gives direct and concise proofs of all results yet avoids the heavy machinery of functional analysis. Moreover, representative examples are treated in some detail.
Author(s): Alain Robert
Series: London Mathematical Society Lecture Note Series
Publisher: CUP
Year: 1983
Language: English
Pages: 215
CONTENTS......Page 5
Foreword......Page 7
Conventional notations and terminology......Page 9
PART I : REPRESENTATIONS OF COMPACT GROUPS......Page 11
1. Compact groups and Haar measures p.......Page 13
Exercises......Page 21
2. Representations, general constructions......Page 23
Exercises......Page 30
3. A geometrical application......Page 31
Exercises......Page 38
4. Finite-dimensional representations of compact groups......Page 39
Peter-Weyl theorem)......Page 48
5. Decomposition of the regular representation......Page 50
Exercises......Page 61
6. Convolution, Plancherel formula & Fourier inversion......Page 63
Exercises......Page 71
7. Characters and group algebras......Page 73
Exercises......Page 86
8. Induced representations and Frobenius-1Veil reciprocity......Page 88
Exercises......Page 99
9. Tannaka duality......Page 100
10. Representations of the rotation group......Page 105
Exercises......Page 117
PART II : REPRESENTATIONS OF LOCALLY COMPACT GROUPS......Page 119
11. Groups with few finite-dimensional representations......Page 121
Exercises......Page 126
12. Invariant measures on locally compact groups and homogeneous spaces......Page 127
Exercises......Page 136
13. Continuity properties of representations......Page 138
14. Representations of G and of L'(G)......Page 143
Exercises......Page 154
15. Schur's lemma : unbounded version......Page 155
Exercises......Page 160
16. Discrete series of locally compact groups......Page 161
Exercises......Page 172
17. The discrete series of S 12 (JR)......Page 174
Exercises......Page 181
18. The principal series of S12OR)......Page 182
19. Decomposition along a commutative subgroup......Page 189
Appendix: Note on Hilbertian integrals......Page 195
20. Type I groups......Page 197
Exercises......Page 203
21. Getting near an abstract Plancherel formula......Page 204
Epilogue......Page 211
References......Page 212
Index......Page 214
