Introduction to the Representation Theory of Compact and Locally Compact Groups

This introduction is designed for graduate students who have some knowledge of finite groups and general topology, but is otherwise self-contained.

Alain Robert (Author)

9780521289757, Cambridge University Press

Paperback, published 10 February 1983

216 pages
22.8 x 15.2 x 1.3 cm, 0.33 kg

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.

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.

Subject Areas: Algebra [PBF]