Introduction to the Representation Theory of Compact and Locally Compact Groups
Introduction to the Representation Theory of Compact and Locally Compact Groups
Alain Robert
February 1983
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9780521289757
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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.
Product details
February 1983Paperback
9780521289757
216 pages
228 × 152 × 13 mm
0.33kg
Available
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.
