0Introduction

II Representation Theory



0 Introduction
The course studies how groups act as groups of linear transformations on vector
spaces. Hopefully, you understand all the words in this sentence. If so, this is a
good start.
In our case, groups are usually either finite groups or topological compact
groups (to be defined later). Topological compact groups are typically subgroups
of the general linear group over some infinite fields. It turns out the tools we
have for finite groups often work well for these particular kinds of infinite groups.
The vector spaces are always finite-dimensional, and usually over C.
Prerequisites of this course include knowledge of group theory (as much as the
IB Groups, Rings and Modules course), linear algebra, and, optionally, geometry,
Galois theory and metric and topological spaces. There is one lemma where
we must use something from Galois theory, but if you don’t know about Galois
theory, you can just assume the lemma to be true without bothering yourself
too much about the proofs.