Representation Theory of Finite Groups

TL;DR

These notes provide a comprehensive introduction to the representation theory of finite groups over complex numbers, emphasizing character theory and illustrating concepts with numerous examples.

Contribution

The notes offer a complete overview of finite group representation theory over complex numbers, highlighting the importance of the base field and including extensive worked examples.

Findings

Thorough coverage of character theory for finite groups

Emphasis on the role of the base field in representation theory

Numerous worked-out examples to illustrate key concepts

Abstract

The point of view of these notes on the topic is to bring out the flavour that Representation Theory is an extension of the first course on Group Theory. We also emphasize the importance of the base field. These notes cover completely the theory over complex numbers which is Character Theory. A large number of worked-out examples are the main feature of these notes. The prerequisite for this note is basic group theory and linear algebra.