Representations and Characters of Groups

."..this is an elegant treatment of ordinary representation theory, at a level suited to undergraduates." M. J. Collins, Times Education Supplement ."..a delightful text, which could be used in a graduate or undergraduate applied mathematics course or to supplement a physics or chemistry course on applications of finite group theory. It is primarily concerned with group algebra and matrix representations which is really what group theory in physics is all about...one can read this book; it is usually not necessary to decipher it. Many of the problems are very challenging, but 52 pages of detailed solutions are given at the end of the book...as a problem source and a supplemental reference on the mathematical details of finite group representations, it is definitely an excellent choice." William Harter, Physics Today

This book provides a modern introduction to the representation theory of finite groups. The theory is developed in terms of modules, since this is appropriate for more advanced work, but considerable emphasis is placed upon constructing characters. The character tables of many groups are given, including all groups of order less than 32, and all but one of the simple groups of order less than 1000. Amongst those applications covered are Burnside's paqb theorem, the use of character theory in studying subgroup structure, and a description of how to use representation theory to investigate molecular vibration. Each chapter is accompanied by a variety of exercises, and full solutions to all the exercises are provided at the end of the book. This will be suitable as a text for those teaching a course in representation theory, and in view of the applications of the subject, will be of interest to chemists and physicists as well as mathematicians.