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.

[ritvikradhakrishnan]

At 12:24 the invariant subspace should be all vectors (a, 0) and not (0, a).

[VicvicW]

Saving this to my library! So many concepts have suddenly clicked upon watching.

Sir, you are a saint

[CiroSantilli]

My dream is to find a video that explains in 15 minutes what's the point of Lie groups/algebras, specifically regarding physics applications. One day.

[davidscott]

Wow! Terrific channel, glad I found it

[kelvinchiu]

16:25 When you write v as that sum, a natural question to ask is what is gv in the first place?

[chenxiaozhou]

How did you compute the trace of a group element without writing out its corresponding matrix? Is there another interpretation for trace aside from the sum of its diagonal elements?

[robertschneider]

Thank you for your awesome lectures! (and work)

[kristianmarinov]

Is there a text to accompany these videos?

[ahmadrezakhazaie]

Sir, Which book do you recommend for learning Representation Theory?

[bennetleff]

Why can't we classify all groups? Is there a proof of this?

[Jaylooker]

Groups acting on mathematical objects are interesting

[سلامعبدالكريممنذورعلي]

Excuse me sir, if you don not mind how can I contact you please