Representation theory Introduction

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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 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