Introduction to the Representation Theory of Compact and Locally Compact Groups Book

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.