Synopses & Reviews
To an algebraist the theory of group characters presents one of those fascinating situations, where the structure of an abstract system is elucidated by a unique set of numbers inherent in the system. But the subject also has a practical aspect, since group characters have gained importance in several branches of science, in which considerations of symmetry play a decisive part. This is an introductory text, suitable for final-year undergraduates or postgraduate students. The only prerequisites are a standard knowledge of linear algebra and a modest acquaintance with group theory. Especial care has been taken to explain how group characters are computed. The character tables of most of the familiar accessible groups are either constructed in the text or included amongst the exercise, all of which are supplied with solutions. The chapter on permutation groups contains a detailed account of the characters of the symmetric group based on the generating function of Frobenius and on the Schur functions. The exposition has been made self-sufficient by the inclusion of auxiliary material on skew-symmetric polynomials, determinants and symmetric functions.
Review
Review of the hardback: 'The author introduces group representations with a commendable balance between the abstract approach emphasising modules and the concrete approach emphasising matrices ...An excellent text!' Mathematical Reviews
Review
Review of the hardback: '... this little volume contains a clear and, at points, brilliant description of the fundamentals of the theory of group characters' Scientia
Synopsis
This is an introductory text, suitable for final-year undergraduates or postgraduate students.
Table of Contents
Preface to the second edition; Preface; 1. Group representations; 2. Elementary properties of group characters; 3. Induced characters; 4. Permutation groups; 5. Group-theoretical applications; 6. Arithmetic properties of group characters; 7. Real representations; Appendix; List of character tables; Solutions; Bibliography; Index.