Introduction to the Representation Theory of Compact and Locally Compact Groups

Table of Contents

Part I. Representations of compact groups:
1. Compact groups and Haar measures
2. Representations, general constructions
3. A geometrical application
4. Finite-dimensional representations of compact groups
5. Decomposition of the regular representation
6. Convolution, Plancherel formula & Fourier inversion
7. Characters and group algebras
8. Induced representations and Frobenius-Weil reciprocity
9. Tannaka duality
10. Representations of the rotation group
Part II. Representations of Locally Compact Groups:
11. Groups with few finite-dimensional representations
12. Invariant measures on locally compact groups and homogeneous spaces
13. Continuity properties of representations
14. Representations of G and of L1(G)
15. Schur's lemma: unbounded version
16. Discrete series of locally compact groups
17. The discrete series of S12(R)
18. The principal series of S12(R)
19. Decomposition along a commutative subgroup
20. Type I groups
21. Getting near an abstract Plancherel formula
Epilogue.

Look Inside

• Table of Contents (66 KB)
• Front Matter (320 KB)
• Copyright Information Page (59 KB)
• Index (103 KB)
• Marketing Excerpt (432 KB)