内容

目次

Part I. Representations of compact groups: 1. Compact groups and Haarmeasures; 2. Representations, general constructions; 3. A geometricalapplication; 4. Finite-dimensional representations of compact groups; 5.Decomposition of the regular representation; 6. Convolution, Plancherelformula & Fourier inversion; 7. Characters and group algebras; 8. Inducedrepresentations and Frobenius-Weil reciprocity; 9. Tannaka duality; 10.Representations of the rotation group; Part II. Representations of LocallyCompact 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 ofL1(G); 15. Schur's lemma: unbounded version; 16. Discrete series of locallycompact groups; 17. The discrete series of S12(R); 18. The principal seriesof S12(R); 19. Decomposition along a commutative subgroup; 20. Type I groups;21. Getting near an abstract Plancherel formula; Epilogue.