Representations and Characters of Groups

This is the second edition of the popular textbook on representation theory of finite groups.

Gordon James (Author), Martin Liebeck (Author)

9780521003926, Cambridge University Press

Paperback, published 18 October 2001

468 pages, 28 b/w illus. 163 tables
23.5 x 15.7 x 2.8 cm, 0.76 kg

'The review found this to be a clearly and carefully written book, which he will recommend to all students seeking an introduction to group representation theory. the authors write in a down-to-earth style, provide a large number of examples throughout, and give very useful content summaries at the end of each chapter … In summary, the additions to the second edition only improve what was already an excellent text.' Proceedings of the Edinburgh Mathematical Society

This book provides a modern introduction to the representation theory of finite groups. Now in its second edition, the authors have revised the text and added much new material. The theory is developed in terms of modules, since this is appropriate for more advanced work, but considerable emphasis is placed upon constructing characters. Included here are the character tables of all groups of order less than 32, and all simple groups of order less than 1000. Applications covered include Burnside's paqb theorem, the use of character theory in studying subgroup structure and permutation groups, and how to use representation theory to investigate molecular vibration. Each chapter features a variety of exercises, with full solutions provided at the end of the book. This will be ideal as a course text in representation theory, and in view of the applications, will be of interest to chemists and physicists as well as mathematicians.

1. Groups and homomorphisms
2. Vector spaces and linear transformations
3. Group representations
4. FG-modules
5. FG-submodules
6. Group algebras
7. FG-homomorphisms
8. Mashcke's theorem
9. Schur's lemma
10. Irreducible modules and the group algebra
11. More on the group algebra
12. Conjugacy classes
13. Characters
14. Inner products of characters
15. The number of irreducible characters
16. Character tables and orthogonality relations
17. Normal subgroups and lifted characters
18. Some elementary character tables
19. Tensor products
20. Restriction to a subgroup
21. Induced modules and characters
22. Algebraic integers
23. Real representations
24. Summary of properties of character tables
25. Characters of groups of order pq
26. Characters of some p-groups
27. Character table of the simple group of order 168
28. Character table of GL(2,q)
29. Permutations and characters
30. Applications to group theory
31. Burnside's theorem
32. An application of representation theory to molecular vibration.

Subject Areas: Groups & group theory [PBG], Algebra [PBF]