This introduction is designed for graduate students who have some knowledge of finite groups and general topology, but is otherwise self-contained.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
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.
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.
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