Representations & Characters of Groups

Rating:
Summary: -Very- highly recommended
Review: Representations and characters of finite groups are a classical subject, with substantial developments well underway a century ago. As a result there has been gradual refinement and polishing of the field. The beauty of this subject is shown well in this book. The style is clear and order of exposition excellent. Moreover, the authors write with great patience, both in respect to presenting calculations in detail and in providing the steps to proofs. This is not to say the book is easy, but rather that the distance from step to step is very well suited for advanced undergraduates and beginning graduate students. The book is highly mathematical in its outlook, except for the final chapter, which deals with normal modes of vibration of a molecule. There are some real gems. In a certain finite group, is it possible to find an element of order two and one of order four whose product has order three? The answer may be found in the chapter, "An Application to Group Theory." The presentation of the Frobenius Reciprocity Theorem is a exceptional delight. As for prerequisites, a good grounding in general group theory at an undergraduate level and a reasonably good acquaintance with rings and modules should suffice.