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Representation theory: Introduction

This lecture is an introduction to representation theory of finite groups. We define linear and permutation representations, and give some examples for the icosahedral group. We then discuss the problem of writing a representation as a sum of smaller ones, which leads to the concept of irreducible ind indecomposable representations. We define the character table of a finite group and work out the character tables of Z/2Z and S3 by inspired guesswork. Finally we mention Burnside's p^aq^b theorem as an application of representation theory. I plan to produce some more videos continuing this one, which will probably appear at totally random times.