Representations Of Finite Groups

Linear Representations of Finite Groups

Representation Theory of Finite Groups

This book is intended to present group representation theory at a level accessible to mature undergraduate students and beginning graduate students. This is achieved by mainly keeping the required background to the level of undergraduate linear algebra, group theory and very basic ring theory. Module theory and Wedderburn theory, as well as tensor products, are deliberately avoided. Instead, we take an approach based on discrete Fourier Analysis. Applications to the spectral theory of graphs are given to help the student appreciate the usefulness of the subject. A number of exercises are included. This book is intended for a 3rd/4th undergraduate course or an introductory graduate course on group representation theory. However, it can also be used as a reference for workers in all areas of mathematics and statistics.

Representations of Finite and Compact Groups

This book is a comprehensive pedagogical presentation of the theory of representation of finite and compact Lie groups that would be of interest to research mathematicians and graduate students interested in group theory and generalizations, topological groups, and Lie groups. Representation theory is discussed on finite groups of rotations, permutation groups, and classical compact Lie groups. The Weyl character formula is proved.